Triangle Seminars
December 2016
Thu
15 Dec 2016
Self-oscillation
Alejandro Jenkins
(Costa Rica U.)
Abstract:
A self-oscillator generates and maintains a periodic motion at the expense of an energy source with no corresponding periodicity. Small perturbations about equilibrium are amplified. Non-linearity accounts for steady-state oscillations and for the ability of coupled self-oscillators to exhibit both spontaneous synchronisation (“entrainmentâ€) and chaos. The theory of self-oscillators has achieved its greatest sophistication in mathematical control theory and in the study of ordinary differential equations. I shall explain in this talk how an understanding better suited to physicists can be founded on considerations of energy, efficiency, and thermodynamic irreversibility.
After reviewing the key differences between forced a parametric resonances on the one hand and self-oscillators on the other, I will comment on how a physical approach to the theory of self-oscillators throws new light on flow instabilities. I will close by describing mechanical and hydrodynamic analogs of the Zel’dovich superradiance of rotating black holes, a subject of considerable interest in high-energy physics today.
A self-oscillator generates and maintains a periodic motion at the expense of an energy source with no corresponding periodicity. Small perturbations about equilibrium are amplified. Non-linearity accounts for steady-state oscillations and for the ability of coupled self-oscillators to exhibit both spontaneous synchronisation (“entrainmentâ€) and chaos. The theory of self-oscillators has achieved its greatest sophistication in mathematical control theory and in the study of ordinary differential equations. I shall explain in this talk how an understanding better suited to physicists can be founded on considerations of energy, efficiency, and thermodynamic irreversibility.
After reviewing the key differences between forced a parametric resonances on the one hand and self-oscillators on the other, I will comment on how a physical approach to the theory of self-oscillators throws new light on flow instabilities. I will close by describing mechanical and hydrodynamic analogs of the Zel’dovich superradiance of rotating black holes, a subject of considerable interest in high-energy physics today.
Posted by: QMW
Wed
14 Dec 2016
On branes and instantons
Ruben Minasian
(IPhT Saclay)
Abstract:
I’ll review old and new aspects of deformed instanton equations derived from D-branes.
I’ll review old and new aspects of deformed instanton equations derived from D-branes.
Posted by: IC
Wed
14 Dec 2016
Scrambling time in eternal BTZ black hole
Andrius Stikonas
(Edinburgh U.)
Abstract:
It is usually hard to compute entanglement entropy and mutual
information for conformal field theories (CFT). Ryu-Takayanagi proposals allows
us to find the same quantities using calculations in gravity. In this talk I
will show how to find holographic entanglement entropy and scrambling time for
BTZ black hole perturbed by a heavy (backreacting) particle. Holographic bulk
description improves on the shock-wave approximation in 3d bulk dimensions. I
will also discuss my work to generalize this calculation to the rotating BTZ
black hole.
It is usually hard to compute entanglement entropy and mutual
information for conformal field theories (CFT). Ryu-Takayanagi proposals allows
us to find the same quantities using calculations in gravity. In this talk I
will show how to find holographic entanglement entropy and scrambling time for
BTZ black hole perturbed by a heavy (backreacting) particle. Holographic bulk
description improves on the shock-wave approximation in 3d bulk dimensions. I
will also discuss my work to generalize this calculation to the rotating BTZ
black hole.
Posted by: QMW
Thu
8 Dec 2016
Classification of surface defects from Little Strings
Nathan Haouzi
(UC Berkeley)
Abstract:
The so-called 6d (2,0) conformal field theory in six dimensions, labeled by an ADE Lie algebra, has become of great interest in recent years. Most notably, it gave new insights into lower dimensional supersymmetric field theories, for instance in four dimensions, after compactification. In this talk, I will talk about a deformation of this CFT, the six-dimensional (2,0) little string theory: its origin lies in type IIB string theory, compactified on an ADE singularity. We further compactify the 6d little string on a Riemann surface with punctures. The resulting defects are D-branes that wrap the 2-cycles of the singularity. This construction has many applications, and I will focus on one: I will provide the little string origin of the classification of surface defects of the 6d (2,0) CFT, for ADE Lie algebras. Furthermore, I will give the physical realization of the so-called Bala-Carter labels that classify nilpotent orbits of these Lie algebras.
The so-called 6d (2,0) conformal field theory in six dimensions, labeled by an ADE Lie algebra, has become of great interest in recent years. Most notably, it gave new insights into lower dimensional supersymmetric field theories, for instance in four dimensions, after compactification. In this talk, I will talk about a deformation of this CFT, the six-dimensional (2,0) little string theory: its origin lies in type IIB string theory, compactified on an ADE singularity. We further compactify the 6d little string on a Riemann surface with punctures. The resulting defects are D-branes that wrap the 2-cycles of the singularity. This construction has many applications, and I will focus on one: I will provide the little string origin of the classification of surface defects of the 6d (2,0) CFT, for ADE Lie algebras. Furthermore, I will give the physical realization of the so-called Bala-Carter labels that classify nilpotent orbits of these Lie algebras.
Posted by: IC
Thu
8 Dec 2016
Symbolic summation assists particle physics
Carsten Schneider
(RISC)
Abstract:
Symbolic summation started with Abramov's telescoping algorithm for rational functions (1971), was pushed further by Gosper's algorithm for hypergeometric expressions (1978) and reached its first peak level with Zeilberger's creative telescoping algorithm (1990) and Petkovsek's recurrence solver (1992) to treat definite hypergeometric sums.
In this talk we focus on the difference ring approach which covers all these algorithms as special cases. Its foundation was lead by Karr's summation algorithm (1981) and has been pushed forward significantly within the last 18 years.
In a long term project with DESY (Deutsches Elektronen-Synchrotron) the produced algorithms have been playing a central role to evaluate several hundred thousands of 2-loop and 3-loop massive Feynman integrals.
In this talk we will elaborate by concrete examples how our advanced difference ring theory and the underlying algorithms encoded within the summation package Sigma are used to attack these highly complicated Feynman integrals.
Symbolic summation started with Abramov's telescoping algorithm for rational functions (1971), was pushed further by Gosper's algorithm for hypergeometric expressions (1978) and reached its first peak level with Zeilberger's creative telescoping algorithm (1990) and Petkovsek's recurrence solver (1992) to treat definite hypergeometric sums.
In this talk we focus on the difference ring approach which covers all these algorithms as special cases. Its foundation was lead by Karr's summation algorithm (1981) and has been pushed forward significantly within the last 18 years.
In a long term project with DESY (Deutsches Elektronen-Synchrotron) the produced algorithms have been playing a central role to evaluate several hundred thousands of 2-loop and 3-loop massive Feynman integrals.
In this talk we will elaborate by concrete examples how our advanced difference ring theory and the underlying algorithms encoded within the summation package Sigma are used to attack these highly complicated Feynman integrals.
Posted by: QMW
Wed
7 Dec 2016
Examples of Berry phase in quantum field theory
📍 London
Vasileios Niarchos
(Durham)
Abstract:
Berry phase is a well-known feature of quantum mechanics. In this talk I will discuss the less-explored subject of Berry phase in quantum field theory. We will see that even simple quantum field theories can exhibit non-trivial Berry phases, and will discuss an explicit example in axion electrodynamics. We will also discuss a general relation between the Berry connection in conformal field theories with non-trivial conformal manifolds and the connections previously considered by several authors in conformal perturbation theory. The implementation of this relation in 2d N=(2,2) and 4d N=2 superconformal field theories leads to a useful re-derivation of the tt* equations.
Berry phase is a well-known feature of quantum mechanics. In this talk I will discuss the less-explored subject of Berry phase in quantum field theory. We will see that even simple quantum field theories can exhibit non-trivial Berry phases, and will discuss an explicit example in axion electrodynamics. We will also discuss a general relation between the Berry connection in conformal field theories with non-trivial conformal manifolds and the connections previously considered by several authors in conformal perturbation theory. The implementation of this relation in 2d N=(2,2) and 4d N=2 superconformal field theories leads to a useful re-derivation of the tt* equations.
Posted by: KCL
Wed
7 Dec 2016
Superstring worldsheet in AdS/CFT: beyond perturbation theory
📍 London
Valentina Forini
(Humboldt, Berlin)
Abstract:
String sigma-models relevant in AdS/CFT are highly non-trivial two-dimensional field theories for which predictions at finite coupling assume integrability and/or the duality itself.
In this framework, I will discuss progress on how to extract finite coupling information via the use of lattice field theory methods.
String sigma-models relevant in AdS/CFT are highly non-trivial two-dimensional field theories for which predictions at finite coupling assume integrability and/or the duality itself.
In this framework, I will discuss progress on how to extract finite coupling information via the use of lattice field theory methods.
Posted by: KCL
Thu
1 Dec 2016
Localised Black Holes and Precision Holography
Jorge Santos
(Cambridge)
Abstract:
We numerically construct asymptotically global AdS_5xS^5 black holes that are localised on the S^5. These are solutions to type IIB supergravity with S^8horizon topology that dominate the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to AdS_5-Schwarzschild x S^5. By the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, this transition is dual to spontaneously breaking the SO(6) R-symmetry of N=4 supersymmetric Yang-Mills down to SO(5). We extrapolate the location of this phase transition and compute the expectation value of a scalar operator in the low energy phase. In addition, we discuss the construction of localised black holes in type IIA, which are dual (via T-duality) to the low temperature phase of thermal 1+1 dimensional supersymmetric Yang-Mills theory on a circle.
We numerically construct asymptotically global AdS_5xS^5 black holes that are localised on the S^5. These are solutions to type IIB supergravity with S^8horizon topology that dominate the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to AdS_5-Schwarzschild x S^5. By the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, this transition is dual to spontaneously breaking the SO(6) R-symmetry of N=4 supersymmetric Yang-Mills down to SO(5). We extrapolate the location of this phase transition and compute the expectation value of a scalar operator in the low energy phase. In addition, we discuss the construction of localised black holes in type IIA, which are dual (via T-duality) to the low temperature phase of thermal 1+1 dimensional supersymmetric Yang-Mills theory on a circle.
Posted by: IC
November 2016
Wed
30 Nov 2016
AdS4 black holes and 3d gauge theories
📍 London
Alberto Zaffaroni
(Milan Bicocca)
Abstract:
One of the great success of string theory is the microscopical explanation of the entropy of a class of asymptotically flat black holes.
Much less is known about asymptotically AdS black holes in four dimensions or higher. In this talk I explain how to derive the entropy of a class of asymptotically AdS supersymmetric black holes in four dimensions using holography. The counting of black hole micro-states is related to a counting of states in the dual 3d gauge theory which can be explicitly
performed using localization.
One of the great success of string theory is the microscopical explanation of the entropy of a class of asymptotically flat black holes.
Much less is known about asymptotically AdS black holes in four dimensions or higher. In this talk I explain how to derive the entropy of a class of asymptotically AdS supersymmetric black holes in four dimensions using holography. The counting of black hole micro-states is related to a counting of states in the dual 3d gauge theory which can be explicitly
performed using localization.
Posted by: KCL
Wed
30 Nov 2016
Hilbert Series and aspects of the moduli space of instantons on CP2
Alessandro Pini
(Oviedo U.)
Abstract:
In the first part of the talk I give an introduction to the computational tool called "Hilbert Series" (HS). I analyze how it can be employed for the characterization of the moduli space of vacua of a QFT and of the moduli space of instantons. Then, in the second part of the talk, I discuss the moduli space of (framed) self-dual instantons on CP^2. These are described by an ADHM-like construction which allows to compute the Hilbert Series of the moduli space. The latter has been found to be blind to certain compact directions. I probe these directions, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover I discuss the ADHM-like construction of instantons on CP^2/Z_n as well as compute its Hilbert series. As in the unorbifolded case, these turn out to coincide with those for instantons on C^2/Z_n. This talk is mainly based on https://arxiv.org/abs/1502.07876 .
In the first part of the talk I give an introduction to the computational tool called "Hilbert Series" (HS). I analyze how it can be employed for the characterization of the moduli space of vacua of a QFT and of the moduli space of instantons. Then, in the second part of the talk, I discuss the moduli space of (framed) self-dual instantons on CP^2. These are described by an ADHM-like construction which allows to compute the Hilbert Series of the moduli space. The latter has been found to be blind to certain compact directions. I probe these directions, finding them to correspond to a Grassmanian, upon considering appropriate ungaugings. Moreover I discuss the ADHM-like construction of instantons on CP^2/Z_n as well as compute its Hilbert series. As in the unorbifolded case, these turn out to coincide with those for instantons on C^2/Z_n. This talk is mainly based on https://arxiv.org/abs/1502.07876 .
Posted by: QMW
Thu
24 Nov 2016
S-matrix bootstrap revisited
Joao Penedones
(Lausanne U.)
Abstract:
Inspired by the recent success of the numerical approach to the conformal bootstrap, we revisit the S-matrix bootstrap program. We shall explain how to obtain analytic bounds on the interaction strength in 1+1 QFT. In higher dimensions, we propose a numerical algorithm that seems to converge to optimal bounds.
Inspired by the recent success of the numerical approach to the conformal bootstrap, we revisit the S-matrix bootstrap program. We shall explain how to obtain analytic bounds on the interaction strength in 1+1 QFT. In higher dimensions, we propose a numerical algorithm that seems to converge to optimal bounds.
Posted by: QMW
Wed
23 Nov 2016
Non-Wilsonian RG flows and the T barT perturbation of 2D quantum field theories
📍 London
Roberto Tateo
(University of Turin)
Abstract:
An interesting link between the effective string theory describing the colour confinement in Yang-Mills theories and conformal field theories perturbed by the composite operator \(T \bar{T}\) was recently discovered. We will discuss various aspects of this special kind of integrable
perturbation and how it affects the energy levels of a generic 2D Quantum Field Theory, through a surprising relation with the inviscid Burgers equation.
As this class of models corresponds to non-Wilsonian RG trajectories, these studies may help to clarify important aspects concerning the appearance of singularities in effective QFT, and hopefully be useful in the effective string framework.
An interesting link between the effective string theory describing the colour confinement in Yang-Mills theories and conformal field theories perturbed by the composite operator \(T \bar{T}\) was recently discovered. We will discuss various aspects of this special kind of integrable
perturbation and how it affects the energy levels of a generic 2D Quantum Field Theory, through a surprising relation with the inviscid Burgers equation.
As this class of models corresponds to non-Wilsonian RG trajectories, these studies may help to clarify important aspects concerning the appearance of singularities in effective QFT, and hopefully be useful in the effective string framework.
Posted by: KCL
Wed
23 Nov 2016
SEMINAR CANCELLED
Paul Townsend
(Cambridge)
Abstract:
The N-extended massless superparticle in a 4D Minkowski background has a worldline time-reversal invariance that becomes CPT in the quantum theory. This symmetry is anomalous for odd N, which explains why there is no CPT-self-conjugate massless supermultiplet for N=1. In the
supertwistor formulation of superparticle mechanics, the anomaly is a close cousin of the parity anomaly of 3D gauge theories. CPT is not anomalous if N is even but if 2N is odd there is a Kramers degeneracy, which explains why the N=2 hypermultiplet is a doubled version of the CPT-self-conjugate supermultiplet of helicities (-1/2,0,0,1/2).
The N-extended massless superparticle in a 4D Minkowski background has a worldline time-reversal invariance that becomes CPT in the quantum theory. This symmetry is anomalous for odd N, which explains why there is no CPT-self-conjugate massless supermultiplet for N=1. In the
supertwistor formulation of superparticle mechanics, the anomaly is a close cousin of the parity anomaly of 3D gauge theories. CPT is not anomalous if N is even but if 2N is odd there is a Kramers degeneracy, which explains why the N=2 hypermultiplet is a doubled version of the CPT-self-conjugate supermultiplet of helicities (-1/2,0,0,1/2).
Posted by: IC
Tue
22 Nov 2016
Black holes and exotic branes in string theory
Masaki Shigemori
(QMUL)
Abstract:
PhD Lecture 4: Black hole microstates and exotic branes: We will discuss supergravity representations of black hole microstates and the possible role played by exotic branes.
PhD Lecture 4: Black hole microstates and exotic branes: We will discuss supergravity representations of black hole microstates and the possible role played by exotic branes.
Posted by: QMW
Mon
21 Nov 2016
Tinkertoys for the Exceptional (2,0) Theories
Jacques Distler
(Texas U.)
Abstract:
I'll give an introduction to N=2, D=4 SCFTs of "Class-S" and a survey of our programme for classifying such theories. I will put special emphasis on the theories arising from the Exceptional (2,0) SCFTs in D=6.
I'll give an introduction to N=2, D=4 SCFTs of "Class-S" and a survey of our programme for classifying such theories. I will put special emphasis on the theories arising from the Exceptional (2,0) SCFTs in D=6.
Posted by: IC
Mon
21 Nov 2016
Black holes and exotic branes in string theory
Masaki Shigemori
(QMUL)
Abstract:
PhD Lecture 3: Exotic branes: We will see that duality predicts various low-codimension objects called exotic branes, and discuss their peculiar properties.
PhD Lecture 3: Exotic branes: We will see that duality predicts various low-codimension objects called exotic branes, and discuss their peculiar properties.
Posted by: QMW
Thu
17 Nov 2016
Recent Advances in Heterotic Moduli
Eirik Eik Svanes
(Paris, LPTHE)
Abstract:
I will discuss recent advances in addressing the heterotic moduli problem in six and seven dimensions. To map out the reduction to a lower dimensional effective theory, and in a quest to complete our understanding of the generically torsional geometries that appear, it is important to understand the moduli of these geometries. I will briefly review the infinitesimal moduli space in six dimensions, and comment on some recent advances in understanding its geometric properties. I will then explain how a similar story is emerging in seven dimensional compactifications on more exotic manifolds with G2-structure, giving hope that similar tools can be applied to understand moduli in other areas of string theory, with possible applications to phenomenology and AdS/CFT. If time, I will comment on some recent advances is studying finite deformations and obstructions of the moduli space.
I will discuss recent advances in addressing the heterotic moduli problem in six and seven dimensions. To map out the reduction to a lower dimensional effective theory, and in a quest to complete our understanding of the generically torsional geometries that appear, it is important to understand the moduli of these geometries. I will briefly review the infinitesimal moduli space in six dimensions, and comment on some recent advances in understanding its geometric properties. I will then explain how a similar story is emerging in seven dimensional compactifications on more exotic manifolds with G2-structure, giving hope that similar tools can be applied to understand moduli in other areas of string theory, with possible applications to phenomenology and AdS/CFT. If time, I will comment on some recent advances is studying finite deformations and obstructions of the moduli space.
Posted by: IC
Thu
17 Nov 2016
Exotic objects from Double Field Theory
Edvard Musaev
(AEI Potsdam)
Abstract:
T-duality is known to generate exotic objects, which cannot be consistently described in terms of conventional supergravity. In the focus of this talk are backgrounds of DFT carrying Q or R fluxes, which are non-commutative and non-associative in the conventional description. We show that the Berman-Rudolph's DFT-monopole solution which unifies the backgrounds of NS5-brane and KK-monopole also describes these exotic backgrounds upon a choice of section condition. The resulting Q- and R-monopoles no longer have non-trivial monodromies and the only sign of non-geometry is a non-trivial dependence of the fields on dual (winding) coordinates.
based on 1607.05450
T-duality is known to generate exotic objects, which cannot be consistently described in terms of conventional supergravity. In the focus of this talk are backgrounds of DFT carrying Q or R fluxes, which are non-commutative and non-associative in the conventional description. We show that the Berman-Rudolph's DFT-monopole solution which unifies the backgrounds of NS5-brane and KK-monopole also describes these exotic backgrounds upon a choice of section condition. The resulting Q- and R-monopoles no longer have non-trivial monodromies and the only sign of non-geometry is a non-trivial dependence of the fields on dual (winding) coordinates.
based on 1607.05450
Posted by: QMW
Wed
16 Nov 2016
Vertex operator algebras from four-dimensional SCFTs
📍 London
Christopher Beem
(Oxford University)
Abstract:
I will review the recently exposed connection between N=2 superconformal field theories in four dimensions and vertex operator algebras (VOAs). I will outline some general features of the VOAs that arise in this manner and describe the manner in which they reflect four-dimensional operations such as gauging and Higgsing. Time permitting, I will also touch on the modular properties of characters of these VOAs.
I will review the recently exposed connection between N=2 superconformal field theories in four dimensions and vertex operator algebras (VOAs). I will outline some general features of the VOAs that arise in this manner and describe the manner in which they reflect four-dimensional operations such as gauging and Higgsing. Time permitting, I will also touch on the modular properties of characters of these VOAs.
Posted by: KCL
Wed
16 Nov 2016
Polygon Seminar: Boundaries, Modules and Symplectic Duality
Mathew Bullimore
(Oxford)
Abstract:
I will discuss connections between supersymmetric gauge theories in three dimensions and an exciting development in representation theory known as symplectic duality. I will focus on the simplest example of this phenomenon, which arises from a U(1) gauge theory with N hypermultiplets.
I will discuss connections between supersymmetric gauge theories in three dimensions and an exciting development in representation theory known as symplectic duality. I will focus on the simplest example of this phenomenon, which arises from a U(1) gauge theory with N hypermultiplets.
Posted by: IC
Tue
15 Nov 2016
Black holes and exotic branes in string theory
Masaki Shigemori
(QMUL)
Abstract:
PhD Lecture 2: Supergravity solutions: We will discuss the supergravity solutions representing various brane configurations and see how the duality transformations are manifested in them.
PhD Lecture 2: Supergravity solutions: We will discuss the supergravity solutions representing various brane configurations and see how the duality transformations are manifested in them.
Posted by: QMW
Mon
14 Nov 2016
Black holes and exotic branes in string theory
Masaki Shigemori
(QMUL)
Abstract:
PhD Lecture 1: String theory and branes: We will review the extended objects in string theory and the duality transformations relating them
PhD Lecture 1: String theory and branes: We will review the extended objects in string theory and the duality transformations relating them
Posted by: QMW
Thu
10 Nov 2016
A magnetically induced quantum critical point in holography
Olga Papadoulaki
(Utrecht)
Abstract:
Abstract:
We are using holography to study quantum phase transitions in a 2+1 D strongly coupled non conformal gauge theory at finite chemical potential and magnetic field B. Our gravity dual is 4D N = 2 Fayet-Iliopoulos gauged supergravity. We found a line of quantum critical points at B= Bc between extremal dyonic black branes and extremal magnetically charged "thermal gas" solutions. We will introduce the two types of solutions, their thermodynamics and their phase diagram. Then we will discuss the physics of the critical point and we will point out qualitative similarities between our field theory and Nambu- Jona- Lasinio model in 2+1 D under the presence of an external magnetic field. We will conclude with some open questions both on the gravity and field theory side and we will discuss future directions.
Abstract:
We are using holography to study quantum phase transitions in a 2+1 D strongly coupled non conformal gauge theory at finite chemical potential and magnetic field B. Our gravity dual is 4D N = 2 Fayet-Iliopoulos gauged supergravity. We found a line of quantum critical points at B= Bc between extremal dyonic black branes and extremal magnetically charged "thermal gas" solutions. We will introduce the two types of solutions, their thermodynamics and their phase diagram. Then we will discuss the physics of the critical point and we will point out qualitative similarities between our field theory and Nambu- Jona- Lasinio model in 2+1 D under the presence of an external magnetic field. We will conclude with some open questions both on the gravity and field theory side and we will discuss future directions.
Posted by: IC
Thu
10 Nov 2016
Twistors and Conformal Higher-Spin Theory
Tristan McLoughlin
(Trinity College Dublin)
Abstract:
Higher-spin fields can play an important role in effective field theories and increasingly are of interest due to their appearance in recent studies of holography.
Understanding their interactions is however often involved and searching for alternative formulations could be very useful. In this talk we will consider
one such formulation, namely twistors. After giving a general introduction to the use of twistors in describing the dynamics of massless field theories, we will focus on the construction of off-shell actions directly in twistor space including a recent higher-spin generalisation of self-dual Weyl gravity. We will show how this formulation produces the expected flat space-time spectrum and linearised symmetries. In analogy with the known embedding of Einstein gravity inside Weyl gravity, we identify a ghost free sub-sector of the conformal higher-spin theory and consider its cubic couplings. Finally we describe proposed anti-self-dual interaction terms to extend the twistor action to the full conformal higher-spin theory.
Higher-spin fields can play an important role in effective field theories and increasingly are of interest due to their appearance in recent studies of holography.
Understanding their interactions is however often involved and searching for alternative formulations could be very useful. In this talk we will consider
one such formulation, namely twistors. After giving a general introduction to the use of twistors in describing the dynamics of massless field theories, we will focus on the construction of off-shell actions directly in twistor space including a recent higher-spin generalisation of self-dual Weyl gravity. We will show how this formulation produces the expected flat space-time spectrum and linearised symmetries. In analogy with the known embedding of Einstein gravity inside Weyl gravity, we identify a ghost free sub-sector of the conformal higher-spin theory and consider its cubic couplings. Finally we describe proposed anti-self-dual interaction terms to extend the twistor action to the full conformal higher-spin theory.
Posted by: QMW
Wed
9 Nov 2016
An algebraic approach to the classification of supergravity backgrounds
📍 London
Jose Miguel Figueroa-O'Farrill
(Edinburgh)
Abstract:
I will report on joint work with Andrea Santi outlining an algebraic reformulation of the classification problem of eleven-dimensional supergravity backgrounds. The basic object of study is the Killing superalgebra of the background, whose algebraic structure has recently been elucidated. If time permits I will also comment on work also involving Paul de Medeiros applying these techniques to the construction of rigidly supersymmetric theories in curved spaces.
I will report on joint work with Andrea Santi outlining an algebraic reformulation of the classification problem of eleven-dimensional supergravity backgrounds. The basic object of study is the Killing superalgebra of the background, whose algebraic structure has recently been elucidated. If time permits I will also comment on work also involving Paul de Medeiros applying these techniques to the construction of rigidly supersymmetric theories in curved spaces.
Posted by: KCL
Wed
9 Nov 2016
Integrable deformations of AdS superstrings
Ben Hoare
(Zurich, ETH)
Abstract:
In this talk I will describe recent progress towards understanding integrable deformations of superstrings in AdS backgrounds. One well-known example of such a deformation is the TsT transformation, which involves a T-duality, a shift introducing the deformation parameter, and a reverse T-duality. After introducing this deformation, I will give two alternative constructions: (i) as a particular non-abelian duality, and (ii) as a particular Yang-Baxter deformation. In the second part of the talk I will outline how this extends to a general relationship between non-abelian duality and Yang-Baxter deformations, and discuss the consequences for the Weyl invariance of the deformed models.
In this talk I will describe recent progress towards understanding integrable deformations of superstrings in AdS backgrounds. One well-known example of such a deformation is the TsT transformation, which involves a T-duality, a shift introducing the deformation parameter, and a reverse T-duality. After introducing this deformation, I will give two alternative constructions: (i) as a particular non-abelian duality, and (ii) as a particular Yang-Baxter deformation. In the second part of the talk I will outline how this extends to a general relationship between non-abelian duality and Yang-Baxter deformations, and discuss the consequences for the Weyl invariance of the deformed models.
Posted by: IC
Thu
3 Nov 2016
Strings and High Energy Scattering
Volker Schomerus
(Desy Hamburg)
Abstract:
The high energy behavior of physical scattering amplitudes challenged early string theory. With the discovery of gauge-string dualities the obstacle was overcome and today string theory provides precision results, in particular for the high energy limit. In my talk I will review the many facets of integrability in high energy scattering at weak, intermediate and strong coupling.
The high energy behavior of physical scattering amplitudes challenged early string theory. With the discovery of gauge-string dualities the obstacle was overcome and today string theory provides precision results, in particular for the high energy limit. In my talk I will review the many facets of integrability in high energy scattering at weak, intermediate and strong coupling.
Posted by: QMW
Wed
2 Nov 2016
Unitarity and positivity constraints for CFT at large N
L. Fernando Alday
(Oxford)
Abstract:
We consider the four-point correlator of the stress tensor multiplet in N = 4 SYM in the limit of large c=N^2, but finite \lambda=g^2 N. For finite values of \lambda single-trace intermediate operators arise at order 1/c and this leads to specific poles in the Mellin representation of the correlator. The sign of the residue at these poles is fixed by unitarity. We consider solutions consistent with crossing symmetry and this pole structure. We show that in a certain regime all solutions result in a negative contribution to the anomalous dimension of twist four operators. This positivity condition can also be proven by assuming the correct Regge behaviour for the Mellin amplitude. The positivity constraints arising from CFT for the Mellin amplitude take a very similar form to the causality constraint for the forward limit of the S-matrix.
We consider the four-point correlator of the stress tensor multiplet in N = 4 SYM in the limit of large c=N^2, but finite \lambda=g^2 N. For finite values of \lambda single-trace intermediate operators arise at order 1/c and this leads to specific poles in the Mellin representation of the correlator. The sign of the residue at these poles is fixed by unitarity. We consider solutions consistent with crossing symmetry and this pole structure. We show that in a certain regime all solutions result in a negative contribution to the anomalous dimension of twist four operators. This positivity condition can also be proven by assuming the correct Regge behaviour for the Mellin amplitude. The positivity constraints arising from CFT for the Mellin amplitude take a very similar form to the causality constraint for the forward limit of the S-matrix.
Posted by: IC
Wed
2 Nov 2016
Towards the string dual of a color superconductor
David Mateos
(Barcelona)
Abstract:
At low temperature and high quark chemical potential, QCD exhibits color superconducting phases, namely phases in which the color gauge symmetry is spontaneously broken. I will describe work in progress aimed at constructing string duals of gauge theories that exhibit these types of phases.
At low temperature and high quark chemical potential, QCD exhibits color superconducting phases, namely phases in which the color gauge symmetry is spontaneously broken. I will describe work in progress aimed at constructing string duals of gauge theories that exhibit these types of phases.
Posted by: IC
October 2016
Fri
28 Oct 2016
Non-Relativistic Scale Anomalies and Geometry
Igal Arav
(Tel Aviv U)
Abstract:
I will discuss the coupling of non-relativistic field theories to curved spacetime, and develop a framework for analyzing the possible structure of non-relativistic (Lifshitz) scale anomalies using a cohomological formulation of the Wess-Zumino consistency condition. I will compare between cases with or without Galilean boost symmetry, and between cases with or without an equal time foliation of spacetime. In 2+1 dimensions with a dynamical critical exponent of z=2, the absence of a foliation structure allows for an A-type anomaly in the Galilean case, but also introduces the possibility of an infinite set of B-type anomalies.
I will also derive Ward identities for flat space correlation functions in Lifshitz field theories, and develop a method for calculating Lifshitz anomaly coefficients from these correlation functions using split dimensional regularization.
I will discuss the coupling of non-relativistic field theories to curved spacetime, and develop a framework for analyzing the possible structure of non-relativistic (Lifshitz) scale anomalies using a cohomological formulation of the Wess-Zumino consistency condition. I will compare between cases with or without Galilean boost symmetry, and between cases with or without an equal time foliation of spacetime. In 2+1 dimensions with a dynamical critical exponent of z=2, the absence of a foliation structure allows for an A-type anomaly in the Galilean case, but also introduces the possibility of an infinite set of B-type anomalies.
I will also derive Ward identities for flat space correlation functions in Lifshitz field theories, and develop a method for calculating Lifshitz anomaly coefficients from these correlation functions using split dimensional regularization.
Posted by: IC
Thu
27 Oct 2016
A c-Theorem for Two-dimensional Boundaries and Defects
Andy O'Bannon
(Southampton)
Abstract:
I will present a proof for a monotonicity theorem, or c-theorem, for a three-dimensional Conformal Field Theory (CFT) on a space with a boundary, and for a higher-dimensional CFT with a two-dimensional defect. The proof is applicable only to renormalization group flows that preserve locality, reflection positivity, and Euclidean invariance along the boundary or defect, and that are localized at the boundary or defect, such that the bulk theory remains conformal along the flow. The method of proof is a generalization of Komargodski’s proof of Zamolodchikov’s c-theorem. The key ingredient is an external “dilaton†field introduced to match Weyl anomalies between the ultra-violet (UV) and infra-red (IR) fixed points. Reflection positivity in the dilaton’s effective action guarantees that a certain coefficient in the boundary/defect Weyl anomaly must take a value in the UV that is larger than (or equal to) the value in the IR. This boundary/defect c-theorem may have important implications for many theoretical and experimental systems, ranging from graphene to branes in string theory and M-theory.
I will present a proof for a monotonicity theorem, or c-theorem, for a three-dimensional Conformal Field Theory (CFT) on a space with a boundary, and for a higher-dimensional CFT with a two-dimensional defect. The proof is applicable only to renormalization group flows that preserve locality, reflection positivity, and Euclidean invariance along the boundary or defect, and that are localized at the boundary or defect, such that the bulk theory remains conformal along the flow. The method of proof is a generalization of Komargodski’s proof of Zamolodchikov’s c-theorem. The key ingredient is an external “dilaton†field introduced to match Weyl anomalies between the ultra-violet (UV) and infra-red (IR) fixed points. Reflection positivity in the dilaton’s effective action guarantees that a certain coefficient in the boundary/defect Weyl anomaly must take a value in the UV that is larger than (or equal to) the value in the IR. This boundary/defect c-theorem may have important implications for many theoretical and experimental systems, ranging from graphene to branes in string theory and M-theory.
Posted by: QMW
Wed
26 Oct 2016
Supersymmetric Localization on AdS2 x S1
📍 London
Rajesh Gupta
(King's College London)
Abstract:
Conformal symmetry relates the metric on AdS_2 x S^1 to that of S^3. This implies that under a suitable choice of boundary conditions for fields on AdS_2 the partition function of conformal field theories on these spaces must agree which makes AdS_2 \times S^1 a good testing ground to study supersymmetric localization on non-compact spaces. We evaluate the partition function of N=2 supersymmetric Chern-Simons theory on AdS_2 x S^1 using localization, where the radius of S^1 is q times that of AdS_2. With boundary conditions on AdS_2 x S^1 which ensure that all the physical fields are normalizable and lie in the space of square integrable wave functions in AdS_2, we find that the result for the partition function precisely agrees with that of the theory on the q-fold covering of S^3.
Conformal symmetry relates the metric on AdS_2 x S^1 to that of S^3. This implies that under a suitable choice of boundary conditions for fields on AdS_2 the partition function of conformal field theories on these spaces must agree which makes AdS_2 \times S^1 a good testing ground to study supersymmetric localization on non-compact spaces. We evaluate the partition function of N=2 supersymmetric Chern-Simons theory on AdS_2 x S^1 using localization, where the radius of S^1 is q times that of AdS_2. With boundary conditions on AdS_2 x S^1 which ensure that all the physical fields are normalizable and lie in the space of square integrable wave functions in AdS_2, we find that the result for the partition function precisely agrees with that of the theory on the q-fold covering of S^3.
Posted by: KCL
Wed
26 Oct 2016
On universality of transport phenomena in holography
Nick Poovuttikul
(Leiden)
Abstract:
In this talk, I will discuss transport phenomena in two classes of theories with holographic dual. In the first part, I will discuss systems where U(1) current is non-conserved due to anomaly and illustrate how one can show that the anomalous conductivities are non-renormalised in a large class of holographic RG flow. The holographic RG flow we considered is generated by arbitrary dilaton potentials and arbitrary higher derivative terms that do not break global symmetries, incorporating coupling constant corrections to the boundary theory in an expansions around infinite coupling. In the second part, I will focus on systems where translational symmetry is broken by slowly varying scalar fields and show that the bound shear viscosity/entropy density is violate. I will also discuss how to understand the violation in the language of forced fluid dynamics.
In this talk, I will discuss transport phenomena in two classes of theories with holographic dual. In the first part, I will discuss systems where U(1) current is non-conserved due to anomaly and illustrate how one can show that the anomalous conductivities are non-renormalised in a large class of holographic RG flow. The holographic RG flow we considered is generated by arbitrary dilaton potentials and arbitrary higher derivative terms that do not break global symmetries, incorporating coupling constant corrections to the boundary theory in an expansions around infinite coupling. In the second part, I will focus on systems where translational symmetry is broken by slowly varying scalar fields and show that the bound shear viscosity/entropy density is violate. I will also discuss how to understand the violation in the language of forced fluid dynamics.
Posted by: IC
Thu
20 Oct 2016
Conformal Higher Spin Theory and Twistor Space Actions
Philipp Haehnel
(Trinity College Dublin)
Abstract:
We give an introduction to twistor theory and construct a twistor action for the self-dual part of conformal higher spin theories by treating the integrability condition for the holomorphic structure of a complex deformation of flat twistor space as the equations of motion of those higher spin fields. Analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, we identify a ghost-free subsector which generates the unique three-point anti-MHV amplitude consistent with Poincaré invariance and helicity constraints.
We give an introduction to twistor theory and construct a twistor action for the self-dual part of conformal higher spin theories by treating the integrability condition for the holomorphic structure of a complex deformation of flat twistor space as the equations of motion of those higher spin fields. Analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, we identify a ghost-free subsector which generates the unique three-point anti-MHV amplitude consistent with Poincaré invariance and helicity constraints.
Posted by: IC
Thu
20 Oct 2016
Hexagon form factors in ABJM
Raul Pereira
(Uppsala)
Abstract:
In this talk I will start by reviewing the hexagon bootstrap program for three-point functions in N=4. Then I will explain how to extend those methods to ABJM theory by considering three-point functions whose vacua preserve SU(1|2)xU(1) symmetry. I will show that this symmetry fully constraints the two-particle hexagon form factor and comment on how to construct the multi-particle hexagon. Finally, I will conclude with a summary of the difficulties in implementing this program for ABJM.
In this talk I will start by reviewing the hexagon bootstrap program for three-point functions in N=4. Then I will explain how to extend those methods to ABJM theory by considering three-point functions whose vacua preserve SU(1|2)xU(1) symmetry. I will show that this symmetry fully constraints the two-particle hexagon form factor and comment on how to construct the multi-particle hexagon. Finally, I will conclude with a summary of the difficulties in implementing this program for ABJM.
Posted by: IC
Wed
19 Oct 2016
Comments on the Space of QFTs
📍 London
Matthew Buican
(Queen Mary University of London)
Abstract:
In the first part of the talk, I will revisit the question of how to decide whether two 4D N=2 superconformal field theories describe the same physics. Time permitting, I will discuss related questions regarding the classification of 2D rational conformal field theories.
In the first part of the talk, I will revisit the question of how to decide whether two 4D N=2 superconformal field theories describe the same physics. Time permitting, I will discuss related questions regarding the classification of 2D rational conformal field theories.
Posted by: KCL
Wed
19 Oct 2016
Polygon Seminar: Algebraic methods for classical integrability
Alessandro Torrielli
(Surrey)
Abstract:
We will review a series of algebraic techniques to describe classically integrable systems, with an eye to their quantisation. The topics we shall attempt to cover will be: 1. General introduction to classical integrability and notion of Lax pair 2. Classical r-matrices and exchange relations 3. Belavin-Drinfeld theorems and classifications 4. Quantisation and elements of algebraic Bethe ansatz
We will review a series of algebraic techniques to describe classically integrable systems, with an eye to their quantisation. The topics we shall attempt to cover will be: 1. General introduction to classical integrability and notion of Lax pair 2. Classical r-matrices and exchange relations 3. Belavin-Drinfeld theorems and classifications 4. Quantisation and elements of algebraic Bethe ansatz
Posted by: QMW
Tue
18 Oct 2016
Symmetry and String theory
Menika Sharma
(Allahabad)
Abstract:
String theory in the tensionless limit is expected to have a large gauge symmetry. By recasting string theory on the AdS background as a generalization of Vasiliev's theory of massless higher-spin fields, it has become possible to understand the nature of this symmetry. In this talk, I will first give an overview of three-dimensional Vasiliev theory and its dual CFT. I will then discuss the current understanding of the symmetry algebra of string theory as well as open problems related to it.
String theory in the tensionless limit is expected to have a large gauge symmetry. By recasting string theory on the AdS background as a generalization of Vasiliev's theory of massless higher-spin fields, it has become possible to understand the nature of this symmetry. In this talk, I will first give an overview of three-dimensional Vasiliev theory and its dual CFT. I will then discuss the current understanding of the symmetry algebra of string theory as well as open problems related to it.
Posted by: KCL
Tue
18 Oct 2016
On the quantization of a string with endpoint particles and the decay width of the hadronic string
Cobi Sonnenschien
(Tel Aviv)
Abstract:
Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons, glueballs and exotic hadrons as strings in four dimensional at space-time. The models are based on a "map" from stringy hadrons of curved holographic confining backgrounds. In the first part of the talk I will review the "derivation" of the models. I will start with a brief reminder of the passage from the original AdS/CFT correspondence to the string/gauge duality of certain favored confining holographic models. I will then describe the string configurations in these holographic backgrounds that correspond to Wilson lines, mesons, baryons, glueballs and exotics. Key ingredients of the four dimensional picture of hadrons are the "string end-point mass" and the "baryonic string vertex". I will determine the classical trajectories of the HISH spectra. I will review the current understanding of the quantization of these hadronic strings. The computation of HISH decay width of hadrons will be described. In the last part of the talk I will summarize the comparison of the outcome of the HISH models with the PDG data about mesons and baryons. I will present the values of the tension, masses and intercepts extracted from best fits to hadron spectra and write down certain predictions for higher excited hadrons. I will present attempts to identify glueballs. The decay width of certain hadrons will be compared with the theoretical calculation. I will suggest a window to the landscape of tetra-quarks and other exotic hadrons.
Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons, glueballs and exotic hadrons as strings in four dimensional at space-time. The models are based on a "map" from stringy hadrons of curved holographic confining backgrounds. In the first part of the talk I will review the "derivation" of the models. I will start with a brief reminder of the passage from the original AdS/CFT correspondence to the string/gauge duality of certain favored confining holographic models. I will then describe the string configurations in these holographic backgrounds that correspond to Wilson lines, mesons, baryons, glueballs and exotics. Key ingredients of the four dimensional picture of hadrons are the "string end-point mass" and the "baryonic string vertex". I will determine the classical trajectories of the HISH spectra. I will review the current understanding of the quantization of these hadronic strings. The computation of HISH decay width of hadrons will be described. In the last part of the talk I will summarize the comparison of the outcome of the HISH models with the PDG data about mesons and baryons. I will present the values of the tension, masses and intercepts extracted from best fits to hadron spectra and write down certain predictions for higher excited hadrons. I will present attempts to identify glueballs. The decay width of certain hadrons will be compared with the theoretical calculation. I will suggest a window to the landscape of tetra-quarks and other exotic hadrons.
Posted by: IC
Tue
18 Oct 2016
The Quantum Hall Zoo
Carl Turner
(DAMTP)
Abstract:
The Quantum Hall Effect is one of the richest phenomena in condensed matter (now featured in no fewer than three Nobel prizes!). I will introduce and explain it, insofar as we understand it. Towards the end, I will say a few words about work to try and rationalise and relate the many models of the effect.
The Quantum Hall Effect is one of the richest phenomena in condensed matter (now featured in no fewer than three Nobel prizes!). I will introduce and explain it, insofar as we understand it. Towards the end, I will say a few words about work to try and rationalise and relate the many models of the effect.
Posted by: KCL
Thu
13 Oct 2016
N=2 super Yang-Mills and the Geometry of Magnetic Monopoles
Andy Royston
(Texas U.)
Abstract:
In this talk we consider BPS states in 4D, N=2 gauge theory in the presence of defects. We give a semiclassical description of these `framed BPS states' in terms of kernels of Dirac operators on moduli spaces of singular monopoles. For both framed and ordinary BPS states we present a conjectural map between the data of the semiclassical construction and the data of the low-energy, quantum-exact Seiberg-Witten description. This map incorporates both perturbative and nonperturbative field theory corrections to the supersymmetric quantum mechanics of the monopole collective coordinates. We use it to translate recent developments in the study of N=2 theories, including wall-crossing formulae and the no-exotics theorem, into geometric statements about the Dirac kernels. The no-exotics theorem implies a broad generalization of Sen's conjecture concerning the existence of L^2 harmonic forms on monopole moduli space. This talk is based on work done in collaboration with Greg Moore and Dieter Van den Bleeken.
In this talk we consider BPS states in 4D, N=2 gauge theory in the presence of defects. We give a semiclassical description of these `framed BPS states' in terms of kernels of Dirac operators on moduli spaces of singular monopoles. For both framed and ordinary BPS states we present a conjectural map between the data of the semiclassical construction and the data of the low-energy, quantum-exact Seiberg-Witten description. This map incorporates both perturbative and nonperturbative field theory corrections to the supersymmetric quantum mechanics of the monopole collective coordinates. We use it to translate recent developments in the study of N=2 theories, including wall-crossing formulae and the no-exotics theorem, into geometric statements about the Dirac kernels. The no-exotics theorem implies a broad generalization of Sen's conjecture concerning the existence of L^2 harmonic forms on monopole moduli space. This talk is based on work done in collaboration with Greg Moore and Dieter Van den Bleeken.
Posted by: QMW
Wed
12 Oct 2016
Vortices and Vermas
📍 London
Matthew Bullimore
(Oxford University)
Abstract:
In 3d gauge theories, monopole operators create and destroy vortices. I will explore this idea in the context of 3d supersymmetric gauge theories in the presence of an omega background, and explain how it leads to a finite version of the AGT correspondence.
In 3d gauge theories, monopole operators create and destroy vortices. I will explore this idea in the context of 3d supersymmetric gauge theories in the presence of an omega background, and explain how it leads to a finite version of the AGT correspondence.
Posted by: KCL
Wed
12 Oct 2016
N=2 super Yang-Mills and the Geometry of Magnetic Monopoles
Andy Royston
(Texas A-M)
Abstract:
In this talk we consider BPS states in 4D, N=2 gauge theory in the presence of defects. We give a semiclassical description of these `framed BPS states' in terms of kernels of Dirac operators on moduli spaces of singular monopoles. For both framed and ordinary BPS states we present a conjectural map between the data of the semiclassical construction and the data of the low-energy, quantum-exact Seiberg-Witten description. This map incorporates both perturbative and nonperturbative field theory corrections to the supersymmetric quantum mechanics of the monopole collective coordinates. We use it to translate recent developments in the study of N=2 theories, including wall-crossing formulae and the no-exotics theorem, into geometric statements about the Dirac kernels. The no-exotics theorem implies a broad generalization of Sen's conjecture concerning the existence of L^2 harmonic forms on monopole moduli space. This talk is based on work done in collaboration with Greg Moore and Dieter Van den Bleeken.
In this talk we consider BPS states in 4D, N=2 gauge theory in the presence of defects. We give a semiclassical description of these `framed BPS states' in terms of kernels of Dirac operators on moduli spaces of singular monopoles. For both framed and ordinary BPS states we present a conjectural map between the data of the semiclassical construction and the data of the low-energy, quantum-exact Seiberg-Witten description. This map incorporates both perturbative and nonperturbative field theory corrections to the supersymmetric quantum mechanics of the monopole collective coordinates. We use it to translate recent developments in the study of N=2 theories, including wall-crossing formulae and the no-exotics theorem, into geometric statements about the Dirac kernels. The no-exotics theorem implies a broad generalization of Sen's conjecture concerning the existence of L^2 harmonic forms on monopole moduli space. This talk is based on work done in collaboration with Greg Moore and Dieter Van den Bleeken.
Posted by: IC
Wed
12 Oct 2016
Covariant quantum spaces and emergent gravity in the IKKT matrix model
Harold Steinacker
(Vienna U.)
Abstract:
We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations
are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin fields.
They arise from an internal structure which can be viewed as a twisted bundle over S^4, leading to a covariant noncommutative geometry.
The linearized 4-dimensional Einstein equations are obtained from the classical matrix model action under certain conditions,
modified by an IR cutoff. Some one-loop contributions to the effective action are computed using the formalism of string states.
We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations
are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin fields.
They arise from an internal structure which can be viewed as a twisted bundle over S^4, leading to a covariant noncommutative geometry.
The linearized 4-dimensional Einstein equations are obtained from the classical matrix model action under certain conditions,
modified by an IR cutoff. Some one-loop contributions to the effective action are computed using the formalism of string states.
Posted by: QMW
Tue
11 Oct 2016
An operator for the zeros of the Riemann zeta function
Dorje Brody
(Brunel)
Abstract:
The Riemann hypothesis asserts that the nontrivial zeros of the Riemann zeta function should be of the form 1/2 + i E_n, where the set of numbers {E_n} are real. The so-called Hilbert-Pólya conjecture assumes that {E_n} should correspond to the eigenvalues of an operator that is Hermitian. The discovery of such an operator, if it exists, thus amounts to providing a proof of the Riemann hypothesis. In 1999 Berry and Keating conjectured that such an operator should correspond to a quantisation of the classical Hamiltonian H = xp. Since then, the Berry-Keating conjecture has been investigated intensely in the literature, but its validity has remained elusive up to now. In this talk I will derive a “Hamiltonian†(a differential operator), whose classical counterpart is H = xp, having the property that with a suitable boundary condition on its eigenstates, the eigenvalues {E_n} correspond to the nontrivial zeros of the Riemann zeta function. This Hamiltonian is not Hermitian, but is symmetric under space-time reflection (PT symmetric) in a special way. A formal argument will be given for the construction of the metric operator to define an inner-product space for the eigenstates, and the formally “Hermitian" counterpart Hamiltonian. The talk is based on the work carried out in collaboration with Carl M. Bender (Washington University) and Markus P. Müller (University of Western Ontario).
The Riemann hypothesis asserts that the nontrivial zeros of the Riemann zeta function should be of the form 1/2 + i E_n, where the set of numbers {E_n} are real. The so-called Hilbert-Pólya conjecture assumes that {E_n} should correspond to the eigenvalues of an operator that is Hermitian. The discovery of such an operator, if it exists, thus amounts to providing a proof of the Riemann hypothesis. In 1999 Berry and Keating conjectured that such an operator should correspond to a quantisation of the classical Hamiltonian H = xp. Since then, the Berry-Keating conjecture has been investigated intensely in the literature, but its validity has remained elusive up to now. In this talk I will derive a “Hamiltonian†(a differential operator), whose classical counterpart is H = xp, having the property that with a suitable boundary condition on its eigenstates, the eigenvalues {E_n} correspond to the nontrivial zeros of the Riemann zeta function. This Hamiltonian is not Hermitian, but is symmetric under space-time reflection (PT symmetric) in a special way. A formal argument will be given for the construction of the metric operator to define an inner-product space for the eigenstates, and the formally “Hermitian" counterpart Hamiltonian. The talk is based on the work carried out in collaboration with Carl M. Bender (Washington University) and Markus P. Müller (University of Western Ontario).
Posted by: KCL
Thu
6 Oct 2016
Geometry = Efficiency? Decoding the DNA of Prediction
John Joseph Carrasco
(CEA)
Abstract:
One can easily be frustrated by the tremendous redundancy in possible physical description. By this I mean the freedom to choose gauge, make field redefinitions, add any amount of auxiliary spectator matter, and the such. Happily we can exploit such freedom to encourage the emergence of a new duality in gauge theories. The existence of a duality between color and kinematics exposes a hidden local double-copy structure inherent to prediction in many theories. This structure weaves its way between theories both formal and phenomenological, from QCD to Gravity, from Chiral Perturbation Theory to Born-Infeld and Volkov-Akulov, and from open to closed superstring theories. The duality is sharpest at the level of the perturbative S-matrix — so I will focus my talk there, although I will also mention some recent provocative work beyond scattering. I will mainly discuss progress and challenges to generically achieving color-dual kinematic representations at the multi-loop level. I present a path forward that introduces, at least temporarily, a redundancy of description that we can exploit to map a set of functional relations to linear ones. I will talk about this approach in terms of a geometric picture involving the graph of local graphs, discussing tradeoffs and applicability to long-standing problems.
One can easily be frustrated by the tremendous redundancy in possible physical description. By this I mean the freedom to choose gauge, make field redefinitions, add any amount of auxiliary spectator matter, and the such. Happily we can exploit such freedom to encourage the emergence of a new duality in gauge theories. The existence of a duality between color and kinematics exposes a hidden local double-copy structure inherent to prediction in many theories. This structure weaves its way between theories both formal and phenomenological, from QCD to Gravity, from Chiral Perturbation Theory to Born-Infeld and Volkov-Akulov, and from open to closed superstring theories. The duality is sharpest at the level of the perturbative S-matrix — so I will focus my talk there, although I will also mention some recent provocative work beyond scattering. I will mainly discuss progress and challenges to generically achieving color-dual kinematic representations at the multi-loop level. I present a path forward that introduces, at least temporarily, a redundancy of description that we can exploit to map a set of functional relations to linear ones. I will talk about this approach in terms of a geometric picture involving the graph of local graphs, discussing tradeoffs and applicability to long-standing problems.
Posted by: QMW
Wed
5 Oct 2016
An operator for the zeros of the Riemann zeta function
📍 London
Brody Dorje
(Imperial College)
Abstract:
The Riemann hypothesis asserts that the nontrivial zeros of the Riemann zeta function should be of the form 1/2 + i E_n, where the set of numbers {E_n} are real. The so-called Hilbert-Pólya conjecture assumes that {E_n} should correspond to the eigenvalues of an operator that is Hermitian. The discovery of such an operator, if it exists, thus amounts to providing a proof of the Riemann hypothesis. In 1999 Berry and Keating conjectured that such an operator should correspond to a quantisation of the classical Hamiltonian H = xp. Since then, the Berry-Keating conjecture has been investigated intensely in the literature, but its validity has remained elusive up to now. In this talk I will derive a "Hamiltonian" (a differential operator), whose classical counterpart is H = xp, having the property that with a suitable boundary condition on its eigenstates, the eigenvalues {E_n} correspond to the nontrivial zeros of the Riemann zeta function. This Hamiltonian is not Hermitian, but is symmetric under space-time reflection (PT symmetric) in a special way. A formal argument will be given for the construction of the metric operator to define an inner-product space for the eigenstates, and the formally "Hermitian" counterpart Hamiltonian. The talk is based on the work carried out in collaboration with Carl M. Bender (Washington University) and Markus P. Mueller (University of Western Ontario).
The Riemann hypothesis asserts that the nontrivial zeros of the Riemann zeta function should be of the form 1/2 + i E_n, where the set of numbers {E_n} are real. The so-called Hilbert-Pólya conjecture assumes that {E_n} should correspond to the eigenvalues of an operator that is Hermitian. The discovery of such an operator, if it exists, thus amounts to providing a proof of the Riemann hypothesis. In 1999 Berry and Keating conjectured that such an operator should correspond to a quantisation of the classical Hamiltonian H = xp. Since then, the Berry-Keating conjecture has been investigated intensely in the literature, but its validity has remained elusive up to now. In this talk I will derive a "Hamiltonian" (a differential operator), whose classical counterpart is H = xp, having the property that with a suitable boundary condition on its eigenstates, the eigenvalues {E_n} correspond to the nontrivial zeros of the Riemann zeta function. This Hamiltonian is not Hermitian, but is symmetric under space-time reflection (PT symmetric) in a special way. A formal argument will be given for the construction of the metric operator to define an inner-product space for the eigenstates, and the formally "Hermitian" counterpart Hamiltonian. The talk is based on the work carried out in collaboration with Carl M. Bender (Washington University) and Markus P. Mueller (University of Western Ontario).
Posted by: KCL
Wed
5 Oct 2016
Holography inspired stringy hadrons
Cobi Sonnenschein
(Tel Aviv University)
Abstract:
Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons, glueballs and exotic hadrons as strings in four dimensional flat space-time. The models are based on a “map†from stringy hadrons of curved holographic conï¬ning backgrounds. In the ï¬rst part of the talk I will review the “derivation†of the models. I will start with a brief reminder of the passage from the original AdS/CFT correspondence to the string/gauge duality of certain favored conï¬ng holographic models. I will then describe the string conï¬gurations in these holographic backgrounds that correspond to Wilson lines, mesons, baryons, glueballs and exotics. Key ingredients of the four dimensional picture of hadrons are the “string end-point mass†and the “baryonic string vertexâ€. I will determine the classical trajectories of the HISH spectra. I will review the current understanding of the quantization of these hadronic strings. The computation of HISH decay width of hadrons will be described. In the last part of the talk I will sum-marize the comparison of the outcome of the HISH models with the PDG data about mesons and baryons. I will present the values of the tension, masses and intercepts extracted from best ï¬ts to hadron spectra and write down certain predictions for higher excited hadrons. I will present attempts to identify glueballs. The decay width of certain hadrons will be compared with the theoretical calculation. I will suggest a window to the landscape of tetra-quarks and other exotic hadrons.
Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons, glueballs and exotic hadrons as strings in four dimensional flat space-time. The models are based on a “map†from stringy hadrons of curved holographic conï¬ning backgrounds. In the ï¬rst part of the talk I will review the “derivation†of the models. I will start with a brief reminder of the passage from the original AdS/CFT correspondence to the string/gauge duality of certain favored conï¬ng holographic models. I will then describe the string conï¬gurations in these holographic backgrounds that correspond to Wilson lines, mesons, baryons, glueballs and exotics. Key ingredients of the four dimensional picture of hadrons are the “string end-point mass†and the “baryonic string vertexâ€. I will determine the classical trajectories of the HISH spectra. I will review the current understanding of the quantization of these hadronic strings. The computation of HISH decay width of hadrons will be described. In the last part of the talk I will sum-marize the comparison of the outcome of the HISH models with the PDG data about mesons and baryons. I will present the values of the tension, masses and intercepts extracted from best ï¬ts to hadron spectra and write down certain predictions for higher excited hadrons. I will present attempts to identify glueballs. The decay width of certain hadrons will be compared with the theoretical calculation. I will suggest a window to the landscape of tetra-quarks and other exotic hadrons.
Posted by: IC
Tue
4 Oct 2016
String Theory as a Spin Chain
Alessandro Torrielli
(Surrey)
Abstract:
In recent years, the discovery of integrable sectors of string theory has expanded the range of models which are solvable by the techniques of the Bethe ansatz and by the general theory of quantum groups. In this talk, we will give an overview of the S-matrix theory involved in the solution of these models, with mention to the problem of massless particles emerging in a particular instance of the AdS/CFT correspondence.
In recent years, the discovery of integrable sectors of string theory has expanded the range of models which are solvable by the techniques of the Bethe ansatz and by the general theory of quantum groups. In this talk, we will give an overview of the S-matrix theory involved in the solution of these models, with mention to the problem of massless particles emerging in a particular instance of the AdS/CFT correspondence.
Posted by: KCL
September 2016
Thu
29 Sep 2016
On the null origin of the ambitwistor string
Eduardo Casali
(Oxford U.)
Abstract:
The Cachazo-He-Yuan (CHY) formulas are a remarkable representation of tree-level massless scattering amplitudes. Similarly to the Twistor String formulas, the CHY formula presents amplitudes as an integrals over the moduli space of Riemann surfaces constrained to the solutions of a set of algebraic equations called the scattering equations. But contrary to the Twistor String formulas, they can be written in for any dimension and for a variety of massless theories. Behind the original CHY formula and the scattering equations lies a 2D CFT called the Ambitwistor String, much like the original Twistor String, this is a chiral CFT in which correlators of vertex operators reproduce the CHY formulas and give a geometric interpretation of the scattering equations. The Ambitwistor string possesses a few peculiar characteristics when viewed as a string theory, its low energy efective action is the same as Type II closed strings but the appearance of the scattering equations suggests a high-energy limit has been taken a la Gross and Mende. Besides, its genus one correlation functions are modular invariant but UV divergent since they correspond to 10D SUGRA amplitudes. In this talk I'll talk about a program started with P. Tourkine in which the Ambitwistor String (and other Twistor Strings) are treated as coming from the tensionless limit of classcial string theories. These are know as null strings and have a long history in the literature. I'll review the null string and its supersymmetric extensions and show how the Ambitwistor String can be obtained from a particular gauge fixing of the null string. In doing so, I'll address the issue of possible inequivalent quantizations of the null string and compare it to the case of the usual string and shed a light its relation to the Ambitwistor String.
The Cachazo-He-Yuan (CHY) formulas are a remarkable representation of tree-level massless scattering amplitudes. Similarly to the Twistor String formulas, the CHY formula presents amplitudes as an integrals over the moduli space of Riemann surfaces constrained to the solutions of a set of algebraic equations called the scattering equations. But contrary to the Twistor String formulas, they can be written in for any dimension and for a variety of massless theories. Behind the original CHY formula and the scattering equations lies a 2D CFT called the Ambitwistor String, much like the original Twistor String, this is a chiral CFT in which correlators of vertex operators reproduce the CHY formulas and give a geometric interpretation of the scattering equations. The Ambitwistor string possesses a few peculiar characteristics when viewed as a string theory, its low energy efective action is the same as Type II closed strings but the appearance of the scattering equations suggests a high-energy limit has been taken a la Gross and Mende. Besides, its genus one correlation functions are modular invariant but UV divergent since they correspond to 10D SUGRA amplitudes. In this talk I'll talk about a program started with P. Tourkine in which the Ambitwistor String (and other Twistor Strings) are treated as coming from the tensionless limit of classcial string theories. These are know as null strings and have a long history in the literature. I'll review the null string and its supersymmetric extensions and show how the Ambitwistor String can be obtained from a particular gauge fixing of the null string. In doing so, I'll address the issue of possible inequivalent quantizations of the null string and compare it to the case of the usual string and shed a light its relation to the Ambitwistor String.
Posted by: QMW
Thu
15 Sep 2016
Holography inspired stringy hadrons
Cobi Sonnenschein
(Tel Aviv University)
Wed
7 Sep 2016
Kounterterms in AdS Gravity
📍 London
Rodrigo Olea Aceituno
(UNAB, Chile)
Abstract:
As an alternative to the Holographic Renormalization procedure in the
context of AdS/CFT correspondence, we introduce a regularization scheme
for AdS gravity based on the addition of boundary terms which are a
given polynomial of the extrinsic and intrinsic curvatures (Kounterterms).
These terms are closely related to either topological invariants or
Chern-Simons densities in the corresponding dimension, they can be
easily generalized to other gravity theories (Einstein-Gauss-Bonnet,
Lovelock, etc.).
We provide a general prescription on how to obtain standard holographic
quantities at the boundary.
We also briefly comment on a possible relation to supersymmetry.
As an alternative to the Holographic Renormalization procedure in the
context of AdS/CFT correspondence, we introduce a regularization scheme
for AdS gravity based on the addition of boundary terms which are a
given polynomial of the extrinsic and intrinsic curvatures (Kounterterms).
These terms are closely related to either topological invariants or
Chern-Simons densities in the corresponding dimension, they can be
easily generalized to other gravity theories (Einstein-Gauss-Bonnet,
Lovelock, etc.).
We provide a general prescription on how to obtain standard holographic
quantities at the boundary.
We also briefly comment on a possible relation to supersymmetry.
Posted by: KCL