Triangle Seminars
December 2013
Thu
12 Dec 2013
Lovelock theory and AdS/CFT
Jose Edelstein
(University of Santiago de Compostela)
Abstract:
Lovelock theory is the natural extension of general relativity to higher dimensions. It can be also thought of as a toy model for ghost-free higher curvature gravity. It admits a family of AdS vacua, most (but not all) of them supporting black holes, that display interesting features such as a generalized variant of the Hawking-Page phase transition. This provides an appealing arena to explore different holographic aspects in the context of the AdS/CFT correspondence which I will discuss in this talk.
Lovelock theory is the natural extension of general relativity to higher dimensions. It can be also thought of as a toy model for ghost-free higher curvature gravity. It admits a family of AdS vacua, most (but not all) of them supporting black holes, that display interesting features such as a generalized variant of the Hawking-Page phase transition. This provides an appealing arena to explore different holographic aspects in the context of the AdS/CFT correspondence which I will discuss in this talk.
Posted by: QMW
Wed
11 Dec 2013
Generalised Structures and Holography
📍 London
Michela Petrini
(LPTHE Paris)
Wed
11 Dec 2013
Gravity duals of N=2 superconformal field theories with no electrostatic description
Konstadinos Siampos
(U. Mons)
Abstract:
We construct the first eleven-dimensional supergravity solutions, which are regular, have no smearing and possess only SO(2,4) x SO(3) x U(1)_R isometry. They are dual to four-dimensional field theories with N = 2 superconformal symmetry. We utilise the Toda frame of self-dual four-dimensional Euclidean metrics with SU(2) rotational symmetry. They are obtained by transforming the Atiyah–Hitchin instanton under SL(2,R) and are expressed in terms of theta functions. The absence of any extra U(1) symmetry, even asymptotically, renders inapplicable the electrostatic description of our solution.
We construct the first eleven-dimensional supergravity solutions, which are regular, have no smearing and possess only SO(2,4) x SO(3) x U(1)_R isometry. They are dual to four-dimensional field theories with N = 2 superconformal symmetry. We utilise the Toda frame of self-dual four-dimensional Euclidean metrics with SU(2) rotational symmetry. They are obtained by transforming the Atiyah–Hitchin instanton under SL(2,R) and are expressed in terms of theta functions. The absence of any extra U(1) symmetry, even asymptotically, renders inapplicable the electrostatic description of our solution.
Posted by: IC
Wed
4 Dec 2013
Holographic Entanglement Entropy and Spacetime Entanglement
📍 London
Rob Myers
(Perimeter)
Abstract:
Holographic entanglement entropy is part of an expanding dialogue has opened between string theorists and physicists in a variety of other fields, eg, condensed matter and nuclear physics. Holographic entanglement entropy also provides an interesting window into the suggestion that quantum entanglement plays an essential role in the emergence of spacetime geometry in theories of quantum gravity. In this lecture, I will review some of the basic aspects of entanglement entropy and holographic entanglement entropy. I will also describe how holographic entanglement entropy leads one to consider associating entanglement entropies with general regions of spacetime in quantum gravity. Finally, I will discuss some recent work to examine this conjecture more precisely in the context of the AdS/CFT correspondence.
Holographic entanglement entropy is part of an expanding dialogue has opened between string theorists and physicists in a variety of other fields, eg, condensed matter and nuclear physics. Holographic entanglement entropy also provides an interesting window into the suggestion that quantum entanglement plays an essential role in the emergence of spacetime geometry in theories of quantum gravity. In this lecture, I will review some of the basic aspects of entanglement entropy and holographic entanglement entropy. I will also describe how holographic entanglement entropy leads one to consider associating entanglement entropies with general regions of spacetime in quantum gravity. Finally, I will discuss some recent work to examine this conjecture more precisely in the context of the AdS/CFT correspondence.
Posted by: KCL
Wed
4 Dec 2013
A QFT viewpoint on entanglement
📍 London
Erik Tonni
(SISSA)
Abstract:
Entanglement of quantum states and its measures play an important role in many areas of theoretical physics. Some techniques about how to deal with entanglement in QFT will be discussed. In particular, the strong subadditivity play the crucial role in the analysis of the "c-theorems" in 1+1 and 2+1 dimensions. We will also consider the twist fields and how they are employed to find analytic results for the entanglement entropies of disjoint intervals and the negativity (a measure of entanglement for mixed states) 1+1 CFTs.
Entanglement of quantum states and its measures play an important role in many areas of theoretical physics. Some techniques about how to deal with entanglement in QFT will be discussed. In particular, the strong subadditivity play the crucial role in the analysis of the "c-theorems" in 1+1 and 2+1 dimensions. We will also consider the twist fields and how they are employed to find analytic results for the entanglement entropies of disjoint intervals and the negativity (a measure of entanglement for mixed states) 1+1 CFTs.
Posted by: KCL
November 2013
Fri
29 Nov 2013
Probes of Entanglement in Extremal Reissner-Nordstrom AdS
Sebastian Fischetti
(UCSB)
Abstract:
We holographically study the entanglement between two CFTs in a thermofield double state at nonzero chemical potential. In the bulk, this entanglement corresponds to entanglement between the two exterior regions of a Reissner-Nordstrom AdS black hole. We will make use of two probes: thermo-mutual information and two-point correlators of scalar operators. In particular, in the zero-temperature limit the entropy density of the black hole remains finite, while neutral correlators and the mutual information of finite regions vanish, implying that these are not good probes of entanglement at zero temperature. However, the correlators of electrically charged scalar operators can be made to remain finite. We comment on the time evolutions of these quantities and other possible applications.
We holographically study the entanglement between two CFTs in a thermofield double state at nonzero chemical potential. In the bulk, this entanglement corresponds to entanglement between the two exterior regions of a Reissner-Nordstrom AdS black hole. We will make use of two probes: thermo-mutual information and two-point correlators of scalar operators. In particular, in the zero-temperature limit the entropy density of the black hole remains finite, while neutral correlators and the mutual information of finite regions vanish, implying that these are not good probes of entanglement at zero temperature. However, the correlators of electrically charged scalar operators can be made to remain finite. We comment on the time evolutions of these quantities and other possible applications.
Posted by: IC
Wed
27 Nov 2013
Lecture on Higher-spin symmetry
📍 London
Nicolas Boulanger
(Mons)
Wed
27 Nov 2013
Coarse-grained entropy and causality in AdS/CFT
William Kelly
(UCSB)
Abstract:
While the emergence of bulk locality in AdS/CFT is not fully understood, progress has been made towards understanding how pieces of the bulk geometry are encoded in subregions of the CFT. Recently, Hubeny and Rangamani have proposed that a modification of the Ryu-Takayanagi entropy called the 'causal holographic information' (so called because extremal surfaces are replaced with causal boundaries) quantifies the minimum information needed to reconstruct certain causally defined bulk regions. I will argue that the boundary dual of the causal holographic information is a coarse-grained entropy which tracks the one-point functions in the associated boundary domain of dependence. The talk will focus on the motivation and evidence for this conjecture as well the prospects for future precision tests.
While the emergence of bulk locality in AdS/CFT is not fully understood, progress has been made towards understanding how pieces of the bulk geometry are encoded in subregions of the CFT. Recently, Hubeny and Rangamani have proposed that a modification of the Ryu-Takayanagi entropy called the 'causal holographic information' (so called because extremal surfaces are replaced with causal boundaries) quantifies the minimum information needed to reconstruct certain causally defined bulk regions. I will argue that the boundary dual of the causal holographic information is a coarse-grained entropy which tracks the one-point functions in the associated boundary domain of dependence. The talk will focus on the motivation and evidence for this conjecture as well the prospects for future precision tests.
Posted by: IC
Tue
26 Nov 2013
TBA
Reinhold Egger
(Düsseldorf)
Mon
25 Nov 2013
Cubic-interaction-induced deformations of higher-spin symmetries
Euihun Joung
(Scuola Normale Superiore)
Abstract:
The deformations of higher-spin symmetries induced by cubic interactions of symmetric massless bosonic fields are analyzed within the metric-like formalism. In particular, we identify a class of couplings which leave the gauge algebra Abelian but deform one (out of three) gauge transformation, and another class of couplings which deform all three gauge transformations in (A)dS but only two in the flat-space limit. The former class is related to higher-spin algebra multiplets (representations of the global algebra). The latter class is what makes (A)dS a distinguished background for higher-spin interactions and includes in particular the gravitational interactions of higher-spin fields, retrospectively accounting for the Fradkin-Vasiliev solution to the Aragone-Deser problem.
The deformations of higher-spin symmetries induced by cubic interactions of symmetric massless bosonic fields are analyzed within the metric-like formalism. In particular, we identify a class of couplings which leave the gauge algebra Abelian but deform one (out of three) gauge transformation, and another class of couplings which deform all three gauge transformations in (A)dS but only two in the flat-space limit. The former class is related to higher-spin algebra multiplets (representations of the global algebra). The latter class is what makes (A)dS a distinguished background for higher-spin interactions and includes in particular the gravitational interactions of higher-spin fields, retrospectively accounting for the Fradkin-Vasiliev solution to the Aragone-Deser problem.
Posted by: IC
Fri
22 Nov 2013
A monotonicity conjecture in holographic RG flows
Flavio Porri
(SISSA)
Abstract:
Recently the existence of a new quantity which decreases along RG-flows of 4d supersymmetric QFT's with R-symmetry has been conjectured. I will analyze this conjecture from a dual supergravity perspective: using some general properties of domain-wall solutions dual to R-symmetric RG flows, I will define a function interpolating between the correct values at the UV and IR fixed points. I will finally test its monotonicity properties in a class of examples.
Recently the existence of a new quantity which decreases along RG-flows of 4d supersymmetric QFT's with R-symmetry has been conjectured. I will analyze this conjecture from a dual supergravity perspective: using some general properties of domain-wall solutions dual to R-symmetric RG flows, I will define a function interpolating between the correct values at the UV and IR fixed points. I will finally test its monotonicity properties in a class of examples.
Posted by: IC
Thu
21 Nov 2013
A monotonicity conjecture in holographic RG flows
Flavio Porri
(INFN)
Abstract:
Abstract: Recently the existence of a new quantity which decreases along RG-flows of 4d supersymmetric QFT's with R-symmetry has been conjectured. I will analyze this conjecture from a dual supergravity perspective:
using some general properties of domain-wall solutions dual to R-symmetric RG flows, I will define a function interpolating between the correct values at the UV and IR fixed points. I will finally test its monotonicity properties in a class of examples.
Abstract: Recently the existence of a new quantity which decreases along RG-flows of 4d supersymmetric QFT's with R-symmetry has been conjectured. I will analyze this conjecture from a dual supergravity perspective:
using some general properties of domain-wall solutions dual to R-symmetric RG flows, I will define a function interpolating between the correct values at the UV and IR fixed points. I will finally test its monotonicity properties in a class of examples.
Posted by: QMW
Wed
20 Nov 2013
A 360-degree view of M5-branes
📍 London
Neil Lambert
(King's College)
Wed
20 Nov 2013
Projective Superspace
Ulf Lindström
(Uppsala)
Abstract:
Superfields in Superspace provide very economical means of representing supermultiplets. However, there are limitations on the possible actions one may construct in standard superspace when the number of supersymmetries grow. In projective superspace, superspace is enlarged with one CP(1) at each point. I will explain how this improves the situation and exemplify.
Superfields in Superspace provide very economical means of representing supermultiplets. However, there are limitations on the possible actions one may construct in standard superspace when the number of supersymmetries grow. In projective superspace, superspace is enlarged with one CP(1) at each point. I will explain how this improves the situation and exemplify.
Posted by: IC
Tue
19 Nov 2013
TBA
Anne-Christine Davis
(DAMTP, Cambridge)
Thu
14 Nov 2013
Higher Spin algebras in different dimensions
Karapet Mkrtchyan
(Scuola Normale Superiore di Pisa)
Abstract:
Higher Spin Algebras are (infinite-dimensional) Lie algebras, that underlie a theory with Higher Spin spectrum. In different space-time dimensions Higher Spin algebras have different properties. I will present a review and some new results on Higher Spin algebras in different dimensions.
Higher Spin Algebras are (infinite-dimensional) Lie algebras, that underlie a theory with Higher Spin spectrum. In different space-time dimensions Higher Spin algebras have different properties. I will present a review and some new results on Higher Spin algebras in different dimensions.
Posted by: IC
Wed
13 Nov 2013
Primordial perturbations from cosmic inflation
📍 London
David Wands
(Portsmouth)
Abstract:
I will review what has become the standard model for the origin of structure in the Universe: quantum fluctuations of a scalar field during a period of accelerated expansion ("inflation") in the very early universe. I will discuss some of the latest observational evidence, including recent results from ESA's Planck satellite, and what this might tell us about the physics of inflation.
I will review what has become the standard model for the origin of structure in the Universe: quantum fluctuations of a scalar field during a period of accelerated expansion ("inflation") in the very early universe. I will discuss some of the latest observational evidence, including recent results from ESA's Planck satellite, and what this might tell us about the physics of inflation.
Posted by: KCL
Tue
12 Nov 2013
Leverhulme lecture: Unoriented quiver theories with flavor
Massimo Bianchi
(INFN)
Tue
12 Nov 2013
TBA
Benoit Vicedo
(Hertfordshire)
Fri
8 Nov 2013
All AdS_7 solutions of type II supergravity
Dario Rosa
(Milano Bicocca)
Abstract:
In M-theory, the only AdS_7 supersymmetric solutions are AdS_7 x S^4 and its orbifolds. We find and classify new supersymmetric solutions of the type AdS_7 x M_3 in type II supergravity. While in IIB none exist, in IIA with Romans mass (which does not lift to M-theory) there are many new ones. We use a pure spinor approach reminiscent of generalized complex geometry. Without the need for any Ansatz, the system determines uniquely the form of the metric and fluxes, up to solving a system of ODEs. Namely, the metric on M_3 is that of an S^2 fibered over an interval; this is consistent with the Sp(1) R-symmetry of the holographically dual (1,0) theory. By including D8 brane sources, one can numerically obtain regular solutions, where topologically M_3 = S^3.
In M-theory, the only AdS_7 supersymmetric solutions are AdS_7 x S^4 and its orbifolds. We find and classify new supersymmetric solutions of the type AdS_7 x M_3 in type II supergravity. While in IIB none exist, in IIA with Romans mass (which does not lift to M-theory) there are many new ones. We use a pure spinor approach reminiscent of generalized complex geometry. Without the need for any Ansatz, the system determines uniquely the form of the metric and fluxes, up to solving a system of ODEs. Namely, the metric on M_3 is that of an S^2 fibered over an interval; this is consistent with the Sp(1) R-symmetry of the holographically dual (1,0) theory. By including D8 brane sources, one can numerically obtain regular solutions, where topologically M_3 = S^3.
Posted by: IC
Thu
7 Nov 2013
On Scale and Conformal Invariance in Four Dimensions
Anatoly Dymarsky
(DAMTP, Cambridge)
Abstract:
I will be discussing the relation between scale and conformal
symmetry in unitary Lorentz invariant QFTs in four dimensions.
I will be discussing the relation between scale and conformal
symmetry in unitary Lorentz invariant QFTs in four dimensions.
Posted by: IC
Thu
7 Nov 2013
Twistor Strings for N=8 Supergravity
David Skinner
(Cambridge)
Abstract:
I'll explain a new way of looking at 4d supergravity –- as a theory of holomorphic maps
into Penrose's twistor space. Allowing twistor space to have N fermionic directions, the
theory is anomaly free when N=8. Via the Penrose transform, the vertex operators
correspond to an N=8 Einstein supergravity multiplet. Conformal symmetry is explicitly
broken by the presence of the infinity twistor in the BRST operator. I will show how to
compute the complete classical S-matrix from worldsheet correlation functions, and
interpret these amplitudes geometrically.
I'll explain a new way of looking at 4d supergravity –- as a theory of holomorphic maps
into Penrose's twistor space. Allowing twistor space to have N fermionic directions, the
theory is anomaly free when N=8. Via the Penrose transform, the vertex operators
correspond to an N=8 Einstein supergravity multiplet. Conformal symmetry is explicitly
broken by the presence of the infinity twistor in the BRST operator. I will show how to
compute the complete classical S-matrix from worldsheet correlation functions, and
interpret these amplitudes geometrically.
Posted by: QMW
Wed
6 Nov 2013
Quantum black hole entropy and the holomorphic prepotential
📍 London
Sameer Murthy
(King's College)
Fri
1 Nov 2013
Dressing the electron star in a holographic superconductor
Thomas Vanel
(LPTHE Jussieu)
Abstract:
Over the last five years, the gauge/gravity correspondence has been applied to describe quantum critical systems at finite density. The simplest model to consider is Einstein-Maxwell gravity, and the ground state of the system is described by Reissner-Nordstrom black hole where all the charge is carried by the black hole. However, it turns out that this solution is unstable to the formation of both fermionic and bosonic matter, corresponding in the dual field theory to the creation of a Fermi surface and the onset of superconductivity, respectively. We consider Einstein-Maxwell system coupled to a perfect fluid of charged fermions and a charged scalar field. In addition to the black hole, electron star and holographic superconductor solutions, we find new asymptotically AdS 4 solutions, dual to 2+1 CFTs at zero temperature and finite chemical potential, which contain both scalar hair and an electron star. We compute the free energy and show that these new solutions are thermodynamically favoured when they exist. Moreover, we find evidence for a continuous phase transition between the holographic superconductor and the new solutions.
Over the last five years, the gauge/gravity correspondence has been applied to describe quantum critical systems at finite density. The simplest model to consider is Einstein-Maxwell gravity, and the ground state of the system is described by Reissner-Nordstrom black hole where all the charge is carried by the black hole. However, it turns out that this solution is unstable to the formation of both fermionic and bosonic matter, corresponding in the dual field theory to the creation of a Fermi surface and the onset of superconductivity, respectively. We consider Einstein-Maxwell system coupled to a perfect fluid of charged fermions and a charged scalar field. In addition to the black hole, electron star and holographic superconductor solutions, we find new asymptotically AdS 4 solutions, dual to 2+1 CFTs at zero temperature and finite chemical potential, which contain both scalar hair and an electron star. We compute the free energy and show that these new solutions are thermodynamically favoured when they exist. Moreover, we find evidence for a continuous phase transition between the holographic superconductor and the new solutions.
Posted by: IC
October 2013
Thu
31 Oct 2013
How many is different? Answer from ideal Bose gas
Jeong-Hyuck Park
(Sogang U.)
Abstract:
How many H2O molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathematical singularity and realize the notion of `Emergence', without resorting to the thermodynamic limit.
ref: arXiv:1310.5580
How many H2O molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathematical singularity and realize the notion of `Emergence', without resorting to the thermodynamic limit.
ref: arXiv:1310.5580
Posted by: QMW
Wed
30 Oct 2013
Twistor Strings for N=8 Supergravity
📍 London
David Skinner
(DAMTP Cambridge)
Abstract:
I'll explain a new way of looking at 4d supergravity –- as a theory of holomorphic maps into Penrose's twistor space. Allowing twistor space to have N fermionic directions, the theory is anomaly free when N=8. Via the Penrose transform, the vertex operators correspond to an N=8 Einstein supergravity multiplet. Conformal symmetry is explicitly broken by the presence of the infinity twistor in the BRST operator. I will show how to compute the complete classical S-matrix from worldsheet correlation functions, and interpret these amplitudes geometrically.
I'll explain a new way of looking at 4d supergravity –- as a theory of holomorphic maps into Penrose's twistor space. Allowing twistor space to have N fermionic directions, the theory is anomaly free when N=8. Via the Penrose transform, the vertex operators correspond to an N=8 Einstein supergravity multiplet. Conformal symmetry is explicitly broken by the presence of the infinity twistor in the BRST operator. I will show how to compute the complete classical S-matrix from worldsheet correlation functions, and interpret these amplitudes geometrically.
Posted by: KCL
Wed
30 Oct 2013
String compactifications, SU(3) structures and smooth compact toric varieties
Magdalena Larfors
(Oxford)
Abstract:
Compactifications of string theory on Calabi-Yau threefolds lead to supersymmetric four-dimensional vacua with unstable moduli. In order to stabilise these moduli, one may introduce background fluxes in the compact 6-manifold. However, such fluxes backreact on the internal geometry so that the Calabi-Yau condition is broken and a weaker condition of reduced structure group is imposed instead. In contrast to the vast number of Calabi-Yau manifolds, few manifolds with the relevant structure group have been constructed, and this lack of examples has left important properties of flux compactifications in obscurity.
In this talk, I will report on recent progress in the construction of SU(3) structures on 6-dimensional smooth compact toric varieties (SCTVs). I will review the topological criterium for the existence of an SU(3) structure on a 6-manifold, which can be fulfilled on an infinite class of SCTVs. Since in string vacua the torsion of the SU(3) structure are constrained, I will then present a method to explicitly construct the SU(3) structure and compute its torsion. I will discuss when parametric choices can be made to tune the torsion classes, and illustrate the construction with several examples.
Compactifications of string theory on Calabi-Yau threefolds lead to supersymmetric four-dimensional vacua with unstable moduli. In order to stabilise these moduli, one may introduce background fluxes in the compact 6-manifold. However, such fluxes backreact on the internal geometry so that the Calabi-Yau condition is broken and a weaker condition of reduced structure group is imposed instead. In contrast to the vast number of Calabi-Yau manifolds, few manifolds with the relevant structure group have been constructed, and this lack of examples has left important properties of flux compactifications in obscurity.
In this talk, I will report on recent progress in the construction of SU(3) structures on 6-dimensional smooth compact toric varieties (SCTVs). I will review the topological criterium for the existence of an SU(3) structure on a 6-manifold, which can be fulfilled on an infinite class of SCTVs. Since in string vacua the torsion of the SU(3) structure are constrained, I will then present a method to explicitly construct the SU(3) structure and compute its torsion. I will discuss when parametric choices can be made to tune the torsion classes, and illustrate the construction with several examples.
Posted by: IC
Tue
29 Oct 2013
On conformal higher spin models
Arkady Tseytlin
(Imperial)
Mon
28 Oct 2013
Gauge theory and Painleve VI
Nikita Nekrasov
(IHES and Simons Center)
Fri
25 Oct 2013
Instantons on Special Geometries
Maike Tormählen
(Hannover and City U.)
Abstract:
Instantons in higher-dimensional gauge theories appear, for example, in the context of string compactification. The instanton condition on the compact part of spacetime ensures supersymmetry preservation. My aim is to better understand instantons on special holonomy manifolds. I introduce higher-dimensional instantons and show how the instanton condition can be rewritten as a set of differential equations and algebraic conditions. These equations can be solved under certain simplifying assumptions. The algebraic conditions can be interpreted as relations of a certain quiver gauge theory. I describe the construction of these quivers and show that the instanton conditions match the quiver relations.
Instantons in higher-dimensional gauge theories appear, for example, in the context of string compactification. The instanton condition on the compact part of spacetime ensures supersymmetry preservation. My aim is to better understand instantons on special holonomy manifolds. I introduce higher-dimensional instantons and show how the instanton condition can be rewritten as a set of differential equations and algebraic conditions. These equations can be solved under certain simplifying assumptions. The algebraic conditions can be interpreted as relations of a certain quiver gauge theory. I describe the construction of these quivers and show that the instanton conditions match the quiver relations.
Posted by: IC
Thu
24 Oct 2013
Four point correlation functions and 5-point amplitudes
Paul Heslop
(Durham University)
Abstract:
Abstract:
There has been much progress in understanding the four-point
correlator of Stress Energy multiplets in N=4 SYM recently. I will
discuss recent progress in evaluating high loop Feynman integrals
using leading singularities, asymptotics and the symbol. This is used
to evaluate the three-loop four-point correlation function from its
integrand. Then I will show how the full (parity even and odd) 5-point
amplitude can be found from the same four-point correlator integrand.
Abstract:
There has been much progress in understanding the four-point
correlator of Stress Energy multiplets in N=4 SYM recently. I will
discuss recent progress in evaluating high loop Feynman integrals
using leading singularities, asymptotics and the symbol. This is used
to evaluate the three-loop four-point correlation function from its
integrand. Then I will show how the full (parity even and odd) 5-point
amplitude can be found from the same four-point correlator integrand.
Posted by: QMW
Wed
23 Oct 2013
Conformal Bootstrap, the 3d Ising Model, and the Epsilon-expansion
📍 London
Slava Rychkov
(CERN and ENS and Univ.Paris 6)
Abstract:
A classic problem in field theory is to compute the critical exponents of the second-order phase transitions in 3d, for example for the Ising model universality class. Traditionally, this problem has been approached via RG-based techniques, such as the Wilson-Fisher epsilon-expansion. Here I will discuss another method to extract the critical exponents, and more, by using conformal field theory.
A classic problem in field theory is to compute the critical exponents of the second-order phase transitions in 3d, for example for the Ising model universality class. Traditionally, this problem has been approached via RG-based techniques, such as the Wilson-Fisher epsilon-expansion. Here I will discuss another method to extract the critical exponents, and more, by using conformal field theory.
Posted by: KCL
Wed
23 Oct 2013
Resurgence in QFT: the Principal Chiral Model
Daniele Dorigoni
(DAMTP, Cambridge)
Abstract:
I will review the concept of Borel transform and resurgence behavior for the perturbative expansion of generic physical observables presenting particular examples coming from quantum mechanics and supersymmetric localized QFT.
I will then discuss more in details the physical role of non-perturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for non-perturbative saddles in such theories. However, resurgence theory, unifying perturbative and non-perturbative physics, predicts the existence of several types of non-perturbative saddles associated with features of the large-order structure of perturbation theory. These points are illustrated in the PCM, where we found new non-perturbative fractionalized saddle point field configurations, and give a quantum interpretation of previously discovered `uniton’ unstable classical solutions.
I will review the concept of Borel transform and resurgence behavior for the perturbative expansion of generic physical observables presenting particular examples coming from quantum mechanics and supersymmetric localized QFT.
I will then discuss more in details the physical role of non-perturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for non-perturbative saddles in such theories. However, resurgence theory, unifying perturbative and non-perturbative physics, predicts the existence of several types of non-perturbative saddles associated with features of the large-order structure of perturbation theory. These points are illustrated in the PCM, where we found new non-perturbative fractionalized saddle point field configurations, and give a quantum interpretation of previously discovered `uniton’ unstable classical solutions.
Posted by: IC
Tue
22 Oct 2013
Exact representations of Susceptible-Infectious-Removed (SIR) epidemic dynamics on networks
Kieran Sharkey
(Liverpool)
Abstract:
The majority of epidemic models fall into two categories: 1) deterministic models represented by differential equations and 2) stochastic models which can be evaluated by simulation. In this presentation I will discuss the precise connection between these models. Until recently, exact correspondence was only established in situations exhibiting large degrees of symmetry or for infinite populations.
I will consider SIR dynamics on finite static contact networks. I will give an overview of two provably exact deterministic representations of the underlying stochastic model for tree-like networks. These are the message passing description of Karrer and Newman and my pair-based moment closure representation. I will discuss the relationship between the two representations and the relative merits of both.
The majority of epidemic models fall into two categories: 1) deterministic models represented by differential equations and 2) stochastic models which can be evaluated by simulation. In this presentation I will discuss the precise connection between these models. Until recently, exact correspondence was only established in situations exhibiting large degrees of symmetry or for infinite populations.
I will consider SIR dynamics on finite static contact networks. I will give an overview of two provably exact deterministic representations of the underlying stochastic model for tree-like networks. These are the message passing description of Karrer and Newman and my pair-based moment closure representation. I will discuss the relationship between the two representations and the relative merits of both.
Posted by: KCL
Thu
17 Oct 2013
Holographic Conductivity
David Tong
(Cambridge)
Abstract:
I'll review some progress over the past 18 months in computing Ohm's law using holography.
I'll review some progress over the past 18 months in computing Ohm's law using holography.
Posted by: QMW
Wed
16 Oct 2013
3D Bosonization and Chern-Simons Vector Models
📍 London
Guy Gur-Ari
(Weizmann Institute)
Abstract:
Chern-Simons theories coupled to vector matter exhibit interesting phenomena. In the planar limit, these theories are conjectured to be holographically dual to generalized theories of gravity, involving high-spin fields. This is a weak-weak holographic duality that is in some aspects very simple, and may serve as a toy model for deepening our understanding of both holography and string theory. On the CFT side, exact calculations performed in the planar limit, along with constraints imposed by a ‘slightly-broken’ high-spin symmetry, have led to many exact results. These have uncovered the details of a 3D bosonization duality, relating theories with bosonic matter to theories with fermionic matter. I will present dynamical evidence for this duality.
Chern-Simons theories coupled to vector matter exhibit interesting phenomena. In the planar limit, these theories are conjectured to be holographically dual to generalized theories of gravity, involving high-spin fields. This is a weak-weak holographic duality that is in some aspects very simple, and may serve as a toy model for deepening our understanding of both holography and string theory. On the CFT side, exact calculations performed in the planar limit, along with constraints imposed by a ‘slightly-broken’ high-spin symmetry, have led to many exact results. These have uncovered the details of a 3D bosonization duality, relating theories with bosonic matter to theories with fermionic matter. I will present dynamical evidence for this duality.
Posted by: KCL
Wed
16 Oct 2013
A New Class of QFTs: from D-branes to On-Shell Diagrams
Sebastian Franco
(Durham)
Abstract:
Over the last decade, we have witnessed remarkable progress in our understanding of Quantum Field Theories. New insights have emerged from a multitude of fronts, ranging from the Gauge/Gravity Correspondence to Integrability. In this seminar I will discuss Bipartite Field Theories (BFTs), a new class of QFTs embodying many of these new approaches. BFTs are 4d, N=1 quiver gauge theories with Lagrangians defined by bipartite graphs on Riemann surfaces. Remarkably, they underlie a wide spectrum of interesting physical systems, including: D-branes probing Calabi-Yau manifolds, their mirror configurations, integrable systems in (0+1) dimensions and scattering amplitudes in N=4 SYM. I will introduce new techniques for studying these gauge theories. I will explain how their dynamics is captured graphically and the interesting emergence of concepts such as Calabi-Yau manifolds, the Grassmannian and cluster algebras in the classification of IR fixed points. Finally, I will introduce a new framework for analyzing general systems of D3 and D7-branes over toric Calabi-Yau 3-folds. These ideas can be exploited for embedding BFTs in String Theory but have a much wider range of applicability.
Over the last decade, we have witnessed remarkable progress in our understanding of Quantum Field Theories. New insights have emerged from a multitude of fronts, ranging from the Gauge/Gravity Correspondence to Integrability. In this seminar I will discuss Bipartite Field Theories (BFTs), a new class of QFTs embodying many of these new approaches. BFTs are 4d, N=1 quiver gauge theories with Lagrangians defined by bipartite graphs on Riemann surfaces. Remarkably, they underlie a wide spectrum of interesting physical systems, including: D-branes probing Calabi-Yau manifolds, their mirror configurations, integrable systems in (0+1) dimensions and scattering amplitudes in N=4 SYM. I will introduce new techniques for studying these gauge theories. I will explain how their dynamics is captured graphically and the interesting emergence of concepts such as Calabi-Yau manifolds, the Grassmannian and cluster algebras in the classification of IR fixed points. Finally, I will introduce a new framework for analyzing general systems of D3 and D7-branes over toric Calabi-Yau 3-folds. These ideas can be exploited for embedding BFTs in String Theory but have a much wider range of applicability.
Posted by: IC
Tue
15 Oct 2013
TBA
Joan Simon
(Edinburgh)
Fri
11 Oct 2013
Lifshitz as a deformation of Anti-de Sitter
Yegor Korovin
(UvA and Southampton)
Abstract:
We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. Тhe holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the z=1 theory. We set up the holographic dictionary for Einstein-Proca models and explain how renormalization turns the relativistic conformal invariance into non-relativistic Lifshitz invariance with dynamical exponent z=1+epsilon^2. Using only QFT arguments we show that a particular class of deformations of CFTs generically leads to Lifshitz scaling invariance and we provide examples of such deformations. An analytic Lifshitz black brane up to second order in ε is constructed. Relation to some top-down construction will be discussed. Based on 1304.7776 and 1306.3344.
We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. Тhe holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the z=1 theory. We set up the holographic dictionary for Einstein-Proca models and explain how renormalization turns the relativistic conformal invariance into non-relativistic Lifshitz invariance with dynamical exponent z=1+epsilon^2. Using only QFT arguments we show that a particular class of deformations of CFTs generically leads to Lifshitz scaling invariance and we provide examples of such deformations. An analytic Lifshitz black brane up to second order in ε is constructed. Relation to some top-down construction will be discussed. Based on 1304.7776 and 1306.3344.
Posted by: IC
Wed
9 Oct 2013
Higher Spin correlators
Alday Fernando
(Oxford)
Abstract:
I will discuss the three-point correlator of two protected scalar operators and one higher spin twist-two operator in N = 4 SYM, in the limit of large spin. This structure constant can be extracted from the OPE of the four-point correlator of protected scalar operators. Based on the OPE structure, symmetry arguments and intuition from the available perturbative results, it is possible to predict the structure constant at all loops in perturbation theory. Furthermore, this allows also to propose an expression for the all loops four-point correlator in a particular limit.
I will discuss the three-point correlator of two protected scalar operators and one higher spin twist-two operator in N = 4 SYM, in the limit of large spin. This structure constant can be extracted from the OPE of the four-point correlator of protected scalar operators. Based on the OPE structure, symmetry arguments and intuition from the available perturbative results, it is possible to predict the structure constant at all loops in perturbation theory. Furthermore, this allows also to propose an expression for the all loops four-point correlator in a particular limit.
Posted by: KCL
Wed
9 Oct 2013
An Update on Moonshine
Miranda Cheng
(Paris VI)
Abstract:
In 2010, Eguchi–Ooguri–Tachikawa observed an unexpected relation between K3 elliptic genus and the sporadic group M24. In this talk I'll briefly review the recent developments on the topic of moonshine. In particular I will describe a more general relation between mock modular forms and finite groups, using Niemeier lattices as the starting point and including the M24 observation as a special case. I will also discuss various approaches in attempting to understand these mysterious relations, focusing on the study of compactification of heterotic strings on K3 surfaces. This talk will be based on joint work with Duncan–Harvey and with Dong–Harrison–Kachru–Whalen–Wrase.
In 2010, Eguchi–Ooguri–Tachikawa observed an unexpected relation between K3 elliptic genus and the sporadic group M24. In this talk I'll briefly review the recent developments on the topic of moonshine. In particular I will describe a more general relation between mock modular forms and finite groups, using Niemeier lattices as the starting point and including the M24 observation as a special case. I will also discuss various approaches in attempting to understand these mysterious relations, focusing on the study of compactification of heterotic strings on K3 surfaces. This talk will be based on joint work with Duncan–Harvey and with Dong–Harrison–Kachru–Whalen–Wrase.
Posted by: KCL
Tue
8 Oct 2013
TBA
Lionel Mason
(Oxford)
Thu
3 Oct 2013
TBA
Henning Samtleben
(Lyon, Ecole Normale Superieure )
Wed
2 Oct 2013
3d non-abelian mirror symmetry for Wilson loops in matrix models
📍 London
Benjamin Assel
(King's College)
Abstract:
We study half-BPS Wilson loops in D = 3 N =4 gauge theories using matrix models obtained from localization techniques. The infrared CFTs of the N=4 theories are subject to 3-dimensional mirror symmetry, which exchanges the Higgs and Coulomb branches of vacua of dual theories. Recently progress have been made in understanding the mapping of BPS Wilson loops under mirror symmetry in abelian theories. Our aim is to understand the operators dual to half-BPS Wilson loops in non-abelian theories. We propose a matrix model for the mirror loops by implementing mirror symmetry directly in the matrix model and we verify the mapping of loop operators by computing explicitly the Wilson loops and mirror loops in non-abelian linear quiver theories. We discuss the possible gauge theory operators that would lead to the matrix model we found. Our results are nicely related to the brane realization of linear quivers in IIB string theory.
We study half-BPS Wilson loops in D = 3 N =4 gauge theories using matrix models obtained from localization techniques. The infrared CFTs of the N=4 theories are subject to 3-dimensional mirror symmetry, which exchanges the Higgs and Coulomb branches of vacua of dual theories. Recently progress have been made in understanding the mapping of BPS Wilson loops under mirror symmetry in abelian theories. Our aim is to understand the operators dual to half-BPS Wilson loops in non-abelian theories. We propose a matrix model for the mirror loops by implementing mirror symmetry directly in the matrix model and we verify the mapping of loop operators by computing explicitly the Wilson loops and mirror loops in non-abelian linear quiver theories. We discuss the possible gauge theory operators that would lead to the matrix model we found. Our results are nicely related to the brane realization of linear quivers in IIB string theory.
Posted by: KCL
Wed
2 Oct 2013
Universal scaling properties of holographic cohesive phases
Blaise Gouteraux
(Nordita)
Abstract:
In this talk, we focus on strongly-coupled, translation-invariant holographic phases at finite density. We show that they can be classified according to the scaling behavior of the metric, the electric potential and the electric flux, introducing to new scaling exponents (cohesion and conduction). Solutions fall into two classes, depending on whether they break relativistic symmetry or not. We show that the dimensions of IR operators are governed by the new scaling exponents, as well as the low-frequency scaling of the optical conductivity. We show that thermodynamically stable phases are always gapless. Finally, we examine a refinement of the holographic entanglement entropy sensitive to the IR behaviour of the electric flux, and show that the minimal surface thus obtained can be different from the Ryu-Takayanagi proposal depending on the cohesion exponent.
In this talk, we focus on strongly-coupled, translation-invariant holographic phases at finite density. We show that they can be classified according to the scaling behavior of the metric, the electric potential and the electric flux, introducing to new scaling exponents (cohesion and conduction). Solutions fall into two classes, depending on whether they break relativistic symmetry or not. We show that the dimensions of IR operators are governed by the new scaling exponents, as well as the low-frequency scaling of the optical conductivity. We show that thermodynamically stable phases are always gapless. Finally, we examine a refinement of the holographic entanglement entropy sensitive to the IR behaviour of the electric flux, and show that the minimal surface thus obtained can be different from the Ryu-Takayanagi proposal depending on the cohesion exponent.
Posted by: IC
Wed
2 Oct 2013
TBA
Michele Cirafici
(Lisbon)
Tue
1 Oct 2013
Unconsciously rational: optimal strategies in human mental searches in online auctions
Andrea Baronchelli
(City University London)
Abstract:
Characterizing how we explore abstract spaces is key to understand our (ir)rational behavior and decision making. While some light has been shed on the navigation of semantic networks, however, little is known about the mental exploration of metric spaces, such as the one dimensional line of numbers, prices, etc. Here we address this issue by investigating the behavior of users exploring the “bid space” in online auctions. We find that they systematically perform Lévy flights, i.e., random walks whose step lengths follow a power-law distribution. Interestingly, this is the best strategy that can be adopted by a random searcher looking for a target in an unknown environment, and has been observed in the foraging patterns of many species. In the case of online auctions, we measure the power-law scaling over several decades, providing the neatest observation of Lévy flights reported so far. We also show that the histogram describing single individual exponents is well peaked, pointing out the existence of an almost universal behaviour. Furthermore, a simple model reveals that the observed exponents are nearly optimal, and represent a Nash equilibrium. We rationalize these findings through a simple evolutionary process, showing that the observed behavior is robust against invasion of alternative strategies. Our results show that humans share with the other animals universal patterns in general searching processes, and raise fundamental issues in cognitive, behavioural and evolutionary sciences.
Characterizing how we explore abstract spaces is key to understand our (ir)rational behavior and decision making. While some light has been shed on the navigation of semantic networks, however, little is known about the mental exploration of metric spaces, such as the one dimensional line of numbers, prices, etc. Here we address this issue by investigating the behavior of users exploring the “bid space” in online auctions. We find that they systematically perform Lévy flights, i.e., random walks whose step lengths follow a power-law distribution. Interestingly, this is the best strategy that can be adopted by a random searcher looking for a target in an unknown environment, and has been observed in the foraging patterns of many species. In the case of online auctions, we measure the power-law scaling over several decades, providing the neatest observation of Lévy flights reported so far. We also show that the histogram describing single individual exponents is well peaked, pointing out the existence of an almost universal behaviour. Furthermore, a simple model reveals that the observed exponents are nearly optimal, and represent a Nash equilibrium. We rationalize these findings through a simple evolutionary process, showing that the observed behavior is robust against invasion of alternative strategies. Our results show that humans share with the other animals universal patterns in general searching processes, and raise fundamental issues in cognitive, behavioural and evolutionary sciences.
Posted by: KCL
September 2013
Thu
26 Sep 2013
Scale and conformal invariance
📍 London
Zohar Komargodski
(Weizmann Institute)
Wed
11 Sep 2013
Constraints on 2d CFT partition functions
📍 London
Christoph Keller
(Rutgers)
Abstract:
We discuss partition functions of 2d conformal field theories. Modular invariance is known to constrain the spectrum of such theories. We investigate these constraints systematically, using the linear functional method to put new improved upper bounds on the lowest gap in the spectrum. We also consider generalized partition functions of N = (2,2) superconformal theories and discuss the application of our results to Calabi-Yau compactifications.
This talk is based on 1209.4649 with H.Ooguri and 1307.6562 with D.Friedan.
We discuss partition functions of 2d conformal field theories. Modular invariance is known to constrain the spectrum of such theories. We investigate these constraints systematically, using the linear functional method to put new improved upper bounds on the lowest gap in the spectrum. We also consider generalized partition functions of N = (2,2) superconformal theories and discuss the application of our results to Calabi-Yau compactifications.
This talk is based on 1209.4649 with H.Ooguri and 1307.6562 with D.Friedan.
Posted by: KCL