Triangle Seminars
December 2018
Tue
18 Dec 2018
TBA
Tommi Tenkanen
(QMUL)
Thu
13 Dec 2018
Genus-One String Amplitudes from Conformal Field Theory
Luis Fernando Alday
(Oxford)
Wed
12 Dec 2018
An Etude on 3d N=2 Conformal Manifolds
๐ London
Nikolay Bobev
( KU Leuven)
Abstract:
I will describe the one-dimensional complex conformal manifold that controls the infrared dynamics of a three-dimensional N=2 supersymmetric theory of three chiral superfields with a cubic superpotential. Two special points on this conformal manifold are the XYZ model and three decoupled copies of the critical Wess-Zumino model. The conformal manifold enjoys a discrete duality group and can be thought of as an orbifold of CP^1. I will discuss how to compute the spectrum of low lying operators and their OPE coefficients as a function of the coordinate on the conformal manifold using the epsilon-expansion and the numerical conformal bootstrap.
I will describe the one-dimensional complex conformal manifold that controls the infrared dynamics of a three-dimensional N=2 supersymmetric theory of three chiral superfields with a cubic superpotential. Two special points on this conformal manifold are the XYZ model and three decoupled copies of the critical Wess-Zumino model. The conformal manifold enjoys a discrete duality group and can be thought of as an orbifold of CP^1. I will discuss how to compute the spectrum of low lying operators and their OPE coefficients as a function of the coordinate on the conformal manifold using the epsilon-expansion and the numerical conformal bootstrap.
Posted by: KCL
Wed
5 Dec 2018
Graphene and Boundary Conformal Field Theory
Christopher Herzog
(KCL)
Abstract:
The infrared fixed point of graphene under the renormalization group flow is a relatively under studied yet important example of a boundary conformal field theory with a number of remarkable properties. It has a close relationship with three dimensional QED. It maps to itself under electric-magnetic duality. Moreover, it along with its supersymmetric cousins all possess an exactly marginal coupling – the charge of the electron – which allows for straightforward perturbative calculations in the weak coupling limit. I will review past work on this model and also discuss my own contributions, which focus on understanding the boundary contributions to the anomalous trace of the stress tensor and their role in helping to understand the structure of boundary conformal field theory.
The infrared fixed point of graphene under the renormalization group flow is a relatively under studied yet important example of a boundary conformal field theory with a number of remarkable properties. It has a close relationship with three dimensional QED. It maps to itself under electric-magnetic duality. Moreover, it along with its supersymmetric cousins all possess an exactly marginal coupling – the charge of the electron – which allows for straightforward perturbative calculations in the weak coupling limit. I will review past work on this model and also discuss my own contributions, which focus on understanding the boundary contributions to the anomalous trace of the stress tensor and their role in helping to understand the structure of boundary conformal field theory.
Posted by: QMW
Wed
5 Dec 2018
How to Build the Thermofield Double State
Diego Hofman
(Amsterdam)
Abstract:
Given two copies of any quantum mechanical system, one may want to prepare them in the thermofield double state for the purpose of studying thermal physics or black holes. However, the thermofield double is a unique entangled pure state and may be difficult to prepare. We propose a local interacting Hamiltonian for the combined system whose ground state is approximately the thermofield double. The energy gap for this Hamiltonian is of order the temperature. Our construction works for any quantum system satisfying the Eigenvalue Thermalization Hypothesis.
Given two copies of any quantum mechanical system, one may want to prepare them in the thermofield double state for the purpose of studying thermal physics or black holes. However, the thermofield double is a unique entangled pure state and may be difficult to prepare. We propose a local interacting Hamiltonian for the combined system whose ground state is approximately the thermofield double. The energy gap for this Hamiltonian is of order the temperature. Our construction works for any quantum system satisfying the Eigenvalue Thermalization Hypothesis.
Posted by: QMW
Tue
4 Dec 2018
Coulomb branches and mock modular forms
๐ London
Giorgios Korpas
(Trinity College, Dublin)
Abstract:
รขโฌลWe revisit Donaldson-Witten theory, that is the N=2 topologically twisted super Yang-Mills theory with gauge group SU(2) or SO(3) on compact 4-manifolds. We study the effective action in the Coulomb branch of the theory and by considering a specific Q-exact deformation to the theory we find interesting connections to mock modular forms. A specific operator of this theory computes the famous Donaldson invariants and our analysis makes their computation more accessible than previously. We also extend these ideas to the case of ramified Donaldson-Witten theory, that is the theory in the presence of embedded surfaces. Our results make calculations of correlation functions of Coulomb branch operators more trackable and we hope that they can help in the search of new 4-manifold invariants.รขโฌย
รขโฌลWe revisit Donaldson-Witten theory, that is the N=2 topologically twisted super Yang-Mills theory with gauge group SU(2) or SO(3) on compact 4-manifolds. We study the effective action in the Coulomb branch of the theory and by considering a specific Q-exact deformation to the theory we find interesting connections to mock modular forms. A specific operator of this theory computes the famous Donaldson invariants and our analysis makes their computation more accessible than previously. We also extend these ideas to the case of ramified Donaldson-Witten theory, that is the theory in the presence of embedded surfaces. Our results make calculations of correlation functions of Coulomb branch operators more trackable and we hope that they can help in the search of new 4-manifold invariants.รขโฌย
Posted by: KCL
November 2018
Thu
29 Nov 2018
Walking, weakly first order phase transitions and complex CFTs
Bernardo Zan
(EPFL Lausanne)
Abstract:
I will discuss walking behavior in gauge theories and weakly first order phase transition in statistical models. Despite being phenomena appearing in very different physical systems, they both show a region of approximate scale invariance. They can be understood as a RG flow passing between two fixed points living at complex couplings, which we call complex CFTs. By using conformal perturbation theory, knowing the conformal data of the complex CFTs allows us to make predictions on the observables of the walking theory. As an example, I will discuss the two dimensional Q-state Potts model with Q>4.
I will discuss walking behavior in gauge theories and weakly first order phase transition in statistical models. Despite being phenomena appearing in very different physical systems, they both show a region of approximate scale invariance. They can be understood as a RG flow passing between two fixed points living at complex couplings, which we call complex CFTs. By using conformal perturbation theory, knowing the conformal data of the complex CFTs allows us to make predictions on the observables of the walking theory. As an example, I will discuss the two dimensional Q-state Potts model with Q>4.
Posted by: QMW
Wed
28 Nov 2018
The Cross Anomalous dimension in N=4 super Yang–Mills
๐ London
Hagen Munkler
(ETH Zurich)
Abstract:
The cross or soft anomalous dimension matrix describes the
renormalization of Wilson loops with a self-intersection
and is an important object in the study of infrared divergences of
scattering amplitudes. I will discuss it for the
case of the Maldacena–Wilson loop in N=4 supersymmetric Yang–Mills
theory, considering both the strong-coupling
description in terms of minimal surfaces in AdS5 as well as the
weak-coupling side up to the two-loop level. In
either case, the coefficients of the cross anomalous dimension matrix
can be expressed in terms of the cusp anomalous
dimension. The strong-coupling description displays a Gross–Ooguri
phase transition and I will argue that the cross
anomalous dimension is an interesting object to study in an
integrability-based approach.
The cross or soft anomalous dimension matrix describes the
renormalization of Wilson loops with a self-intersection
and is an important object in the study of infrared divergences of
scattering amplitudes. I will discuss it for the
case of the Maldacena–Wilson loop in N=4 supersymmetric Yang–Mills
theory, considering both the strong-coupling
description in terms of minimal surfaces in AdS5 as well as the
weak-coupling side up to the two-loop level. In
either case, the coefficients of the cross anomalous dimension matrix
can be expressed in terms of the cusp anomalous
dimension. The strong-coupling description displays a Gross–Ooguri
phase transition and I will argue that the cross
anomalous dimension is an interesting object to study in an
integrability-based approach.
Posted by: KCL
Wed
28 Nov 2018
Reconstructing AdS3/CFT2 correlators
Rodolfo Russo
(QMUL)
Abstract:
The AdS/CFT duality maps supersymmetric heavy operators with
conformal dimension of the order of the central charge to asymptotically
AdS supergravity solutions. I'll show how, by studying the quadratic
fluctuations around such backgrounds, it is possible to derive 4-point
correlators of two light and two heavy states in the supergravity
approximation. Then by using this input, I'll discuss how to reconstruct
standard supergravity correlators between four (single particle)
operators. I'll present some explicit examples in the AdS3 setup relevant
for the duality with the D1-D5 CFT.
The AdS/CFT duality maps supersymmetric heavy operators with
conformal dimension of the order of the central charge to asymptotically
AdS supergravity solutions. I'll show how, by studying the quadratic
fluctuations around such backgrounds, it is possible to derive 4-point
correlators of two light and two heavy states in the supergravity
approximation. Then by using this input, I'll discuss how to reconstruct
standard supergravity correlators between four (single particle)
operators. I'll present some explicit examples in the AdS3 setup relevant
for the duality with the D1-D5 CFT.
Posted by: IC
Fri
23 Nov 2018
Goldstone pairs at the Fermi surface
Alberto Nicolis
(Columbia)
Abstract:
I will adapt the Goldstone theorem to spontaneously broken boosts, and show that, while still predicting gapless Goldstone states, it is quite forgiving regarding the nature of such states. In particular, I will show that while for solids and superfluids the role of the boost Goldstone states is played by phonon single-particle states, for a Fermi liquid such a role is played by the particle-hole continuum, that is, by two-particle states.
I will adapt the Goldstone theorem to spontaneously broken boosts, and show that, while still predicting gapless Goldstone states, it is quite forgiving regarding the nature of such states. In particular, I will show that while for solids and superfluids the role of the boost Goldstone states is played by phonon single-particle states, for a Fermi liquid such a role is played by the particle-hole continuum, that is, by two-particle states.
Posted by: IC
Thu
22 Nov 2018
Holographic relative entropy in infinite-dimensional Hilbert spaces
Monica Kang
(Harvard)
Abstract:
Quantum error correction provides a convenient setup where bulk operators are defined only on a code subspace of the physical Hilbert space of the conformal field theory. I will first reformulate entanglement wedge reconstruction in the language of operator-algebra quantum error correction with infinite-dimensional physical and code Hilbert spaces. I will streamline my proof that for infinite-dimensional Hilbert spaces, the entanglement wedge reconstruction is identical to the equivalence of the boundary and bulk relative entropies. I will discuss its implications for holographic theories with the Reeh-Schlieder theorem.
Quantum error correction provides a convenient setup where bulk operators are defined only on a code subspace of the physical Hilbert space of the conformal field theory. I will first reformulate entanglement wedge reconstruction in the language of operator-algebra quantum error correction with infinite-dimensional physical and code Hilbert spaces. I will streamline my proof that for infinite-dimensional Hilbert spaces, the entanglement wedge reconstruction is identical to the equivalence of the boundary and bulk relative entropies. I will discuss its implications for holographic theories with the Reeh-Schlieder theorem.
Posted by: QMW
Wed
21 Nov 2018
Wilson Surface Central Charge
๐ London
Andy O'Bannon
(University of Southampton)
Abstract:
M-theory is currently our best candidate for a theory of everything, but remains mysterious. We know M-theory has M2- and M5-branes. The low-energy theory on a stack of coincident M2-branes is well-understood: it is maximally supersymmetric Chern-Simons-matter theory. However, the low-energy theory on a stack of coincident M5-branes remains poorly-understood: it is a maximally supersymmetric theory of self-dual strings with zero tension. In this talk I will discuss one type of probe of the M5-brane theory, namely self-dual strings with infinite tension. These play a role analogous to Wilson lines in gauge theories, but are two-dimensional surfaces rather than lines, and hence are called Wilson surfaces. I will describe holographic calculations of entanglement entropy associated with these infinite-tension self-dual strings, from which we extract a key parameter characterizing them, their central charge. This provides a count of the number of massless degrees of freedom living on them, and thus may shed light on some of the fundamental degrees of freedom of M-theory.
M-theory is currently our best candidate for a theory of everything, but remains mysterious. We know M-theory has M2- and M5-branes. The low-energy theory on a stack of coincident M2-branes is well-understood: it is maximally supersymmetric Chern-Simons-matter theory. However, the low-energy theory on a stack of coincident M5-branes remains poorly-understood: it is a maximally supersymmetric theory of self-dual strings with zero tension. In this talk I will discuss one type of probe of the M5-brane theory, namely self-dual strings with infinite tension. These play a role analogous to Wilson lines in gauge theories, but are two-dimensional surfaces rather than lines, and hence are called Wilson surfaces. I will describe holographic calculations of entanglement entropy associated with these infinite-tension self-dual strings, from which we extract a key parameter characterizing them, their central charge. This provides a count of the number of massless degrees of freedom living on them, and thus may shed light on some of the fundamental degrees of freedom of M-theory.
Posted by: KCL
Wed
21 Nov 2018
Polygon Seminar: Hugh Osborn: Seeking fixed points
Hugh Osborn
(DAMTP, Cambridge University)
Abstract:
Fixed points are crucial in understanding the RG flow of quantum field
theories. The conformal bootstrap has proved a wonderful tool in
determining the properties of CFTs at fixed points but tends to require
guidance in terms of what symmetries to impose and what is the spectrum of
relevant operators. Here I review what can be said in general by using the
time honoured epsilon expansion. Although qualitatively this is not
nowadays the most efficient method it provides qualitative information
about possible fixed points. Finding fixed points which cannot be linked to
the epsilon expansion could provide a clue to non Lagrangian theories.
Fixed points are crucial in understanding the RG flow of quantum field
theories. The conformal bootstrap has proved a wonderful tool in
determining the properties of CFTs at fixed points but tends to require
guidance in terms of what symmetries to impose and what is the spectrum of
relevant operators. Here I review what can be said in general by using the
time honoured epsilon expansion. Although qualitatively this is not
nowadays the most efficient method it provides qualitative information
about possible fixed points. Finding fixed points which cannot be linked to
the epsilon expansion could provide a clue to non Lagrangian theories.
Posted by: IC
Wed
21 Nov 2018
Polygon Seminar: Exploring generalised dualities and integrable deformations
Daniel C Thompson
(Swansea)
Abstract:
Extensions of target space T-duality to non-Abelian isometry groups and even to spaces without isometry have found recent utility within the AdS/CFT correspondence and have played a central role in the development of new classes of integrable string backgrounds called \(\eta\) and \(\lambda\)-models. After a pedagogical introduction to the topic I will outline some recent results concerning the open sector of \(\lambda\)-models and the interpretation of these theories within the formalism of double field theory.
Extensions of target space T-duality to non-Abelian isometry groups and even to spaces without isometry have found recent utility within the AdS/CFT correspondence and have played a central role in the development of new classes of integrable string backgrounds called \(\eta\) and \(\lambda\)-models. After a pedagogical introduction to the topic I will outline some recent results concerning the open sector of \(\lambda\)-models and the interpretation of these theories within the formalism of double field theory.
Posted by: IC
Thu
15 Nov 2018
Free Field Realizations from the Higgs Branch
Carlo Meneghelli
(Oxford)
Abstract:
To any four-dimensional N=2 super-conformal field theory (SCFT) one can canonically associate a two-dimensional vertex operator algebra (VOA). This provides a powerful framework for the analysis of SCFTs and leads to surprising predictions for a large new class of VOAs. In this talk I will present remarkable free field realizations of the relevant VOAs which mirror the effective field theory description of the corresponding four dimensional theory on the Higgs branch of its moduli space of vacua.
To any four-dimensional N=2 super-conformal field theory (SCFT) one can canonically associate a two-dimensional vertex operator algebra (VOA). This provides a powerful framework for the analysis of SCFTs and leads to surprising predictions for a large new class of VOAs. In this talk I will present remarkable free field realizations of the relevant VOAs which mirror the effective field theory description of the corresponding four dimensional theory on the Higgs branch of its moduli space of vacua.
Posted by: QMW
Wed
14 Nov 2018
Logarithmic terms in entanglement entropy: black holes, anomalies and boundaries
๐ London
Sergey Solodukhin
(University of Tours)
Abstract:
In my talk I will give a review on the logarithmic terms that appear in the entanglement entropy, their relation to conformal anomaly and
the geometry of the entangling surfaces. I will discuss how the presence of boundaries may effect these terms.
In my talk I will give a review on the logarithmic terms that appear in the entanglement entropy, their relation to conformal anomaly and
the geometry of the entangling surfaces. I will discuss how the presence of boundaries may effect these terms.
Posted by: KCL
Wed
14 Nov 2018
Type-B Formal Higher Spin Gravity
Maxim Grigoriev
(Lebedev Institute of Physics)
Abstract:
We propose non-linear formally consistent equations of motion for the Type-B Higher Spin Gravity that is dual to the free fermion or to the Gross-Neveu model, depending on the boundary conditions. The equations are directly obtained from the first principles: the gauge invariance of the CFT partition function on an arbitrary background. We show that the system has a vacuum solution describing general higher-spin flat backgrounds and demonstrate that the respective linearized system describes propagation of higher-spin fields over such backgrounds, reproducing all the structures that are known to determine nonlinear higher-spin equations.
We propose non-linear formally consistent equations of motion for the Type-B Higher Spin Gravity that is dual to the free fermion or to the Gross-Neveu model, depending on the boundary conditions. The equations are directly obtained from the first principles: the gauge invariance of the CFT partition function on an arbitrary background. We show that the system has a vacuum solution describing general higher-spin flat backgrounds and demonstrate that the respective linearized system describes propagation of higher-spin fields over such backgrounds, reproducing all the structures that are known to determine nonlinear higher-spin equations.
Posted by: IC
Wed
14 Nov 2018
A nAttractor mechanism for AdS(2) quantum gravity.
๐ London
Finn Larsen
(University of Michigan)
Abstract:
We study the nearly AdS(2) geometry of nearly extremal black holes in N = 2 supergravity in four dimensions. In the strictly extreme limit the attractor mechanism for asymptotically flat black holes states that the horizon geometries of these black holes are independent of scalar moduli. We determine the dependence of the near extreme geometry on asymptotic moduli and express the result in simple formulae that generalize the extremal attractor mechanism to nearly extreme black holes. This is a nAttractor mechanism. We discuss the dependence of the near horizon theory on the scales introduced by generic attractor flows.
We study the nearly AdS(2) geometry of nearly extremal black holes in N = 2 supergravity in four dimensions. In the strictly extreme limit the attractor mechanism for asymptotically flat black holes states that the horizon geometries of these black holes are independent of scalar moduli. We determine the dependence of the near extreme geometry on asymptotic moduli and express the result in simple formulae that generalize the extremal attractor mechanism to nearly extreme black holes. This is a nAttractor mechanism. We discuss the dependence of the near horizon theory on the scales introduced by generic attractor flows.
Posted by: KCL
Wed
7 Nov 2018
AdS_2 holography - Mind the Cap!
๐ London
Iosif Bena
(IPHT)
Abstract:
Black holes appear to lead to information loss, thus violating one of the fundamental tenets of Quantum Mechanics. Recent Information-Theory-based arguments imply that information loss can only be avoided if at the scale of the black hole horizon there exists a structure (commonly called fuzzball or firewall) that allows information to escape. I will discuss the highly-unusual properties that this structure must have and how these properties emerge in the realization of this structure in String Theory via branes, fluxes and topology. I will then describe the implication of this structure for AdS_2 holography.
Black holes appear to lead to information loss, thus violating one of the fundamental tenets of Quantum Mechanics. Recent Information-Theory-based arguments imply that information loss can only be avoided if at the scale of the black hole horizon there exists a structure (commonly called fuzzball or firewall) that allows information to escape. I will discuss the highly-unusual properties that this structure must have and how these properties emerge in the realization of this structure in String Theory via branes, fluxes and topology. I will then describe the implication of this structure for AdS_2 holography.
Posted by: sa
Wed
7 Nov 2018
dS vacua and the swampland
๐ London
Timm Wrase
(TUWIEN)
Abstract:
After briefly reviewing dark energy, dS vacua and the standard model of cosmology, I will discuss recent conjectures that say that metastable dS vacua cannot arise in string theory. These conjectures lead to interesting observational predictions and are currently being tested experimentally. On the theoretical side I will discuss the support for these conjectures as well as the status of explicit counter examples like the KKLT and LVS scenario.
After briefly reviewing dark energy, dS vacua and the standard model of cosmology, I will discuss recent conjectures that say that metastable dS vacua cannot arise in string theory. These conjectures lead to interesting observational predictions and are currently being tested experimentally. On the theoretical side I will discuss the support for these conjectures as well as the status of explicit counter examples like the KKLT and LVS scenario.
Posted by: sa
Wed
7 Nov 2018
After-talk reception
๐ London
Every One
(KCL)
Abstract:
After-talk reception at Staff Common Room King's Building
After-talk reception at Staff Common Room King's Building
Posted by: sa
Thu
1 Nov 2018
Twisted BRST quantization and localization in supergravity
Sameer Murthy
(KCL)
Abstract:
Supersymmetric localization is a powerful technique to evaluate a class of functional integrals in supersymmetric field theories. It reduces the functional integral over field space to ordinary integrals over the space of solutions of the off-shell BPS equations. The application of this technique to supergravity suffers from some problems, both conceptual and practical. I will discuss one of the main conceptual problems, namely how to construct the fermionic symmetry with which to localize. I will show how a deformation of the BRST technique allows us to do this. As an application I will then sketch a computation of the one-loop determinant of the super-graviton that enters the localization formula for BPS black hole entropy.
Supersymmetric localization is a powerful technique to evaluate a class of functional integrals in supersymmetric field theories. It reduces the functional integral over field space to ordinary integrals over the space of solutions of the off-shell BPS equations. The application of this technique to supergravity suffers from some problems, both conceptual and practical. I will discuss one of the main conceptual problems, namely how to construct the fermionic symmetry with which to localize. I will show how a deformation of the BRST technique allows us to do this. As an application I will then sketch a computation of the one-loop determinant of the super-graviton that enters the localization formula for BPS black hole entropy.
Posted by: QMW
October 2018
Wed
31 Oct 2018
Effective actions for near extremal black holes and gauge fields in AdS2
๐ London
Ioannis Papadimitriou
(KIAS)
Abstract:
I will discuss consistent reductions of pure AdS gravity in 3D and 5D to 2D and use them to derive effective actions for the near conformal quantum mechanics dual to the near extremal BTZ and Kerr-AdS5 black holes, respectively. The role of AdS2 gauge fields and their boundary conditions will be discussed in detail.
I will discuss consistent reductions of pure AdS gravity in 3D and 5D to 2D and use them to derive effective actions for the near conformal quantum mechanics dual to the near extremal BTZ and Kerr-AdS5 black holes, respectively. The role of AdS2 gauge fields and their boundary conditions will be discussed in detail.
Posted by: KCL
Wed
31 Oct 2018
Entanglement Content of Particle Excitations
Olalla Castro Alvaredo
(City University)
Abstract:
n this talk I will review the results of recent work in collaboration with Cecilia De Fazio, Benjamin Doyon and Istvรยกn M. Szรยฉcsรยฉnyi. We studied the entanglement of excited states consisting of a finite number of particle excitations. More precisely, we studied the difference between the entanglement entropy of such states and that of the ground state in a simple bi-partition of a quantum system, where both the size of the system and of the bi-partition are infinite, but their ratio is finite. We originally studied this problem in massive 1+1 dimensional QFTs where analytic computations were possible. We have found the results to apply more widely, including to higher dimensional free theories. In all cases we find that the increment of entanglement is a simple function of the ratio between region's and system's size only. Such function, turns out to be exactly the entanglement of a qubit state where the coefficients of the state are simply associated with the probabilities of particles being localised in one or the other part of the bi-partition. In this talk I will describe the results in some detail and discuss their domain of applicability. I will also highlight the main QFT techniques that we have used in order to obtain them analytically and present some numerical data.
n this talk I will review the results of recent work in collaboration with Cecilia De Fazio, Benjamin Doyon and Istvรยกn M. Szรยฉcsรยฉnyi. We studied the entanglement of excited states consisting of a finite number of particle excitations. More precisely, we studied the difference between the entanglement entropy of such states and that of the ground state in a simple bi-partition of a quantum system, where both the size of the system and of the bi-partition are infinite, but their ratio is finite. We originally studied this problem in massive 1+1 dimensional QFTs where analytic computations were possible. We have found the results to apply more widely, including to higher dimensional free theories. In all cases we find that the increment of entanglement is a simple function of the ratio between region's and system's size only. Such function, turns out to be exactly the entanglement of a qubit state where the coefficients of the state are simply associated with the probabilities of particles being localised in one or the other part of the bi-partition. In this talk I will describe the results in some detail and discuss their domain of applicability. I will also highlight the main QFT techniques that we have used in order to obtain them analytically and present some numerical data.
Posted by: IC
Thu
25 Oct 2018
Lessons from CFTs on nontrivial manifolds
Anastasios Petkou
(Aristotle University of Thessaloniki)
Abstract:
Even if one knows everything for a conformal field theory on the infinite plane, new data are required to place the same theory in finite geometries. This is a physically relevant question for finite-temperature/finite-size critical systems. I will show in this talk how to apply an OPE inversion formula to thermal two-point functions of bosonic and fermionic CFTs in general odd dimensions. This allows us to analyze in detail the operator spectrum of these theories. The main result is that nontrivial thermal CFTs arise when the thermal mass satisfies an algebraic transcendental equation that ensures the absence of an infinite set of operators from the spectrum. The solutions of these gap equations for general odd dimensions are in general complex numbers and follow a particular pattern. I will argue that this pattern unveils the large-N vacuum structure of the corresponding theories at zero temperature.
Even if one knows everything for a conformal field theory on the infinite plane, new data are required to place the same theory in finite geometries. This is a physically relevant question for finite-temperature/finite-size critical systems. I will show in this talk how to apply an OPE inversion formula to thermal two-point functions of bosonic and fermionic CFTs in general odd dimensions. This allows us to analyze in detail the operator spectrum of these theories. The main result is that nontrivial thermal CFTs arise when the thermal mass satisfies an algebraic transcendental equation that ensures the absence of an infinite set of operators from the spectrum. The solutions of these gap equations for general odd dimensions are in general complex numbers and follow a particular pattern. I will argue that this pattern unveils the large-N vacuum structure of the corresponding theories at zero temperature.
Posted by: QMW
Wed
24 Oct 2018
Conformal field theory in momentum space
๐ London
Kostas Skenderis
(University of Southampton)
Abstract:
I will give an overview of the topic and I will discuss the non-perturbative derivation of 3-point functions of scalar operators, symmetry current and energy momentum tensor in momentum space, including renormalization and anomalies. Based on 1805.12100, 1711.09105, 1510.08442, 1304.7760.
I will give an overview of the topic and I will discuss the non-perturbative derivation of 3-point functions of scalar operators, symmetry current and energy momentum tensor in momentum space, including renormalization and anomalies. Based on 1805.12100, 1711.09105, 1510.08442, 1304.7760.
Posted by: KCL
Wed
17 Oct 2018
Non-planar Scattering Amplitude - Wilson Loop Duality
Alexander Tumanov
(Tel Aviv U.)
Abstract:
Higher order corrections in the 1/N expansion to scattering amplitudes come from the diagrams with higher genus. One way to address these non-trivial topologies is to view them as planar objects glued into non-planar configurations. They can then be "cut" across all the cycles of the corresponding Riemann surface, fixing the momentum flowing in each cycle. This procedure results in a planar object that belongs to a representation of the modular group of the Riemann surface in question. Various techniques developed for the planar amplitudes can be generalized to these cut non-planar ones. We will investigate the scattering amplitude รขโฌโ Wilson loop duality, specifically focusing on the case of the first non-planar correction, 1/N double trace amplitude, which has the topology of a cylinder. Itรขโฌโขs dual space interpretation is a correlator of two infinite Wilson lines subject to a periodicity constraint. We will confirm this duality by a weak coupling perturbative calculation and a strong coupling string worldsheet one. This will allow us to construct the non-planar loop integrands and the BCFW recursion relation they satisfy, as well as to find an interpretation of the dual conformal symmetry in the non-planar sector, which was previously thought to be broken by 1/N corrections. Lastly, we will discuss this result in the framework of the Wilson Loop OPE approach, which allows one to compute expectation values of Wilson loops at any value of the coupling in the form of an expansion around the collinear limit. We claim that this approach can be directly applied to cut non-planar scattering amplitudes, as well as the N=4 SYM form factors, whose dual space interpretation is remarkably similar to the one of the 1/N amplitude correction.
Higher order corrections in the 1/N expansion to scattering amplitudes come from the diagrams with higher genus. One way to address these non-trivial topologies is to view them as planar objects glued into non-planar configurations. They can then be "cut" across all the cycles of the corresponding Riemann surface, fixing the momentum flowing in each cycle. This procedure results in a planar object that belongs to a representation of the modular group of the Riemann surface in question. Various techniques developed for the planar amplitudes can be generalized to these cut non-planar ones. We will investigate the scattering amplitude รขโฌโ Wilson loop duality, specifically focusing on the case of the first non-planar correction, 1/N double trace amplitude, which has the topology of a cylinder. Itรขโฌโขs dual space interpretation is a correlator of two infinite Wilson lines subject to a periodicity constraint. We will confirm this duality by a weak coupling perturbative calculation and a strong coupling string worldsheet one. This will allow us to construct the non-planar loop integrands and the BCFW recursion relation they satisfy, as well as to find an interpretation of the dual conformal symmetry in the non-planar sector, which was previously thought to be broken by 1/N corrections. Lastly, we will discuss this result in the framework of the Wilson Loop OPE approach, which allows one to compute expectation values of Wilson loops at any value of the coupling in the form of an expansion around the collinear limit. We claim that this approach can be directly applied to cut non-planar scattering amplitudes, as well as the N=4 SYM form factors, whose dual space interpretation is remarkably similar to the one of the 1/N amplitude correction.
Posted by: QMW
Wed
17 Oct 2018
Twisting and localization in supergravity: equivariant cohomology of BPS black holes
๐ London
Imtak Jeon
(KCL)
Abstract:
We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge Q, obeying Q2=H, where H is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the QV deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2รโS2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.
We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge Q, obeying Q2=H, where H is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the QV deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS2รโS2 saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.
Posted by: KCL
Wed
17 Oct 2018
Aspects of de Sitter spacetimes
Dionysios Anninos
(Amsterdam)
Abstract:
We overview some aspects of asymptotically de Sitter spacetimes at the classical and quantum level. We discuss some features of the late time de Sitter wavefunction. We briefly touch upon some properties of the relation between de Sitter space and Euclidean conformal theories, broadly referred to as the dS/CFT correspondence. Finally, time permitting, we will discuss some similarities and differences between the cosmological dS horizon and a more standard black hole horizon.
We overview some aspects of asymptotically de Sitter spacetimes at the classical and quantum level. We discuss some features of the late time de Sitter wavefunction. We briefly touch upon some properties of the relation between de Sitter space and Euclidean conformal theories, broadly referred to as the dS/CFT correspondence. Finally, time permitting, we will discuss some similarities and differences between the cosmological dS horizon and a more standard black hole horizon.
Posted by: QMW
Thu
11 Oct 2018
Some lessons from/for Supergravity in AdS4/CFT3
Costantin Bachas
(ENS Paris)
Abstract:
I will first review the AdS4/SCFT3 correspondence with N=4
supersymmetry. I will then focus on two special aspects which are important in exploring the string landscape:
(1) The existence of N=2 moduli and their fate in gauged supergravity;
(2) Special degeneration limits for which the low-energy limit is a theory of bigravity or massive gravity.
I will first review the AdS4/SCFT3 correspondence with N=4
supersymmetry. I will then focus on two special aspects which are important in exploring the string landscape:
(1) The existence of N=2 moduli and their fate in gauged supergravity;
(2) Special degeneration limits for which the low-energy limit is a theory of bigravity or massive gravity.
Posted by: QMW
Wed
10 Oct 2018
Connecting the weak gravity conjecture to the weak cosmic censorship
๐ London
Jorge Santos
(University of Cambridge)
Abstract:
I will describe some counterexamples to (weak) cosmic censorship in anti-de Sitter spacetime that have been found recently. These are solutions in which the curvature grows without bound in a region of spacetime visible to infinity. I will also discuss a surprising connection between some of these counterexamples and an apparently unrelated conjecture called the weak gravity conjecture.
I will describe some counterexamples to (weak) cosmic censorship in anti-de Sitter spacetime that have been found recently. These are solutions in which the curvature grows without bound in a region of spacetime visible to infinity. I will also discuss a surprising connection between some of these counterexamples and an apparently unrelated conjecture called the weak gravity conjecture.
Posted by: KCL
Wed
10 Oct 2018
Topologically twisted indices and holography
Alberto Zaffaroni
(INFN, Milan Bicocca U.)
Abstract:
Abstract: We define indices for topologically twisted supersymmetric theories from two to five dimensions.
We apply them to the holographic study of AdS black holes, black strings and domain-walls
across dimensions.
Abstract: We define indices for topologically twisted supersymmetric theories from two to five dimensions.
We apply them to the holographic study of AdS black holes, black strings and domain-walls
across dimensions.
Posted by: IC
Thu
4 Oct 2018
Disconnected gauge theories
Diego Rodriguez-Gomez
(Oviedo U.)
Abstract:
Disconnected gauge groups have been, at least comparatively, very poorly studied. Yet they may hide very interesting Physics. Recently, a class of gauge theories based on a particular type of disconnected gauge groups, namely principal extensions, has been introduced. Interestingly, such theories naturally implement the gauging of charge conjugation. In this talk, we will describe such construction and study aspects of its Physics. A particularly spectacular by-product of the construction is that these theories have non-freely generated Coulomb branches, thus providing the first counterexample of the long standing standard lore that Coulomb branch are all freely generated.
Disconnected gauge groups have been, at least comparatively, very poorly studied. Yet they may hide very interesting Physics. Recently, a class of gauge theories based on a particular type of disconnected gauge groups, namely principal extensions, has been introduced. Interestingly, such theories naturally implement the gauging of charge conjugation. In this talk, we will describe such construction and study aspects of its Physics. A particularly spectacular by-product of the construction is that these theories have non-freely generated Coulomb branches, thus providing the first counterexample of the long standing standard lore that Coulomb branch are all freely generated.
Posted by: QMW
Tue
2 Oct 2018
Relating duality covariant approaches to higher derivatives in the heterotic string
Diego Marques
(Buenos Aires)
Abstract:
There are two approaches to duality covariant first order alpha-prime corrections to the heterotic string. One is based on an extension of the duality structure, and the other relies on deformed gauge transformations. I will introduce an all order framework from which both approaches can be derived, proving their equivalence and extending them to higher orders.
There are two approaches to duality covariant first order alpha-prime corrections to the heterotic string. One is based on an extension of the duality structure, and the other relies on deformed gauge transformations. I will introduce an all order framework from which both approaches can be derived, proving their equivalence and extending them to higher orders.
Posted by: IC
September 2018
Thu
27 Sep 2018
Amplitudes and hidden symmetries in supersymmetric Chern-Simons matter theories
Karthik Inbasekar
(Tel Aviv U.)
Abstract:
Chern-Simons theories coupled to fundamental matter have a wide variety of applications ranging from Quantum Hall effect to Quantum gravity via AdS/CFT. These theories enjoy a strong weak duality that has been tested to a very good accuracy via large N computations, such as thermal partition functions, and S matrices. Supersymmetric Chern-Simons theories are equally interesting since they have a self duality and relate to non-supersymmetric theories via RG flows. In the N=2,3 supersymmetric Chern-Simons matter theories, the four point amplitude computed to all orders in the 't Hooft coupling is not renormalised! It is a unique situation in a quantum field theory that the scattering amplitude doesn't receive loop corrections. This indicates the presence of powerful symmetry structures within the theory. This also suggests that higher point amplitudes may be easier to compute using four point amplitudes as building blocks. These higher point amplitudes not only serve as a testing tool for duality but also a probe into the symmetry structure of the theory. As a first step towards this goal, we begin by computing arbitrary n point tree level amplitudes in the N=2 theory via BCFW recursion relations. We then show that the four point tree level amplitude enjoys a dual superconformal symmetry. Since the all loop four point amplitude is tree level exact, it follows that the dual superconformal symmetry is exact to all loops. This is in contrast to highly supersymmetric examples such as N=4 SYM and N=6 ABJM, where the dual superconformal symmetry is in general anomalous. Furthermore, we show that the superconformal and dual superconformal symmetries generate an infinite dimensional Yangian symmetry for the four point amplitude. If these symmetries persist to higher point amplitudes, this suggests that the N=2 superconformal Chern-Simons matter theory may be integrable.
Chern-Simons theories coupled to fundamental matter have a wide variety of applications ranging from Quantum Hall effect to Quantum gravity via AdS/CFT. These theories enjoy a strong weak duality that has been tested to a very good accuracy via large N computations, such as thermal partition functions, and S matrices. Supersymmetric Chern-Simons theories are equally interesting since they have a self duality and relate to non-supersymmetric theories via RG flows. In the N=2,3 supersymmetric Chern-Simons matter theories, the four point amplitude computed to all orders in the 't Hooft coupling is not renormalised! It is a unique situation in a quantum field theory that the scattering amplitude doesn't receive loop corrections. This indicates the presence of powerful symmetry structures within the theory. This also suggests that higher point amplitudes may be easier to compute using four point amplitudes as building blocks. These higher point amplitudes not only serve as a testing tool for duality but also a probe into the symmetry structure of the theory. As a first step towards this goal, we begin by computing arbitrary n point tree level amplitudes in the N=2 theory via BCFW recursion relations. We then show that the four point tree level amplitude enjoys a dual superconformal symmetry. Since the all loop four point amplitude is tree level exact, it follows that the dual superconformal symmetry is exact to all loops. This is in contrast to highly supersymmetric examples such as N=4 SYM and N=6 ABJM, where the dual superconformal symmetry is in general anomalous. Furthermore, we show that the superconformal and dual superconformal symmetries generate an infinite dimensional Yangian symmetry for the four point amplitude. If these symmetries persist to higher point amplitudes, this suggests that the N=2 superconformal Chern-Simons matter theory may be integrable.
Posted by: QMW
Wed
26 Sep 2018
Gravitational free energy in topological AdS/CFT
๐ London
Paul Richmond
(King's College London)
Abstract:
TBA
TBA
Posted by: KCL
Wed
26 Sep 2018
Amplitudes and hidden symmetries in supersymmetric Chern-Simons matter theories
Karthik Inbasekar
(Tel Aviv University)
Abstract:
Chern-Simons theories coupled to fundamental matter have a wide variety of applications ranging from Quantum Hall effect to Quantum gravity via AdS/CFT. These theories enjoy a strong weak duality that has been tested to a very good accuracy via large N computations, such as thermal partition functions, and S matrices. Supersymmetric Chern-Simons theories are equally interesting since they have a self duality and relate to non-supersymmetric theories via RG flows. In the N=2,3 supersymmetric Chern-Simons matter theories, the four point amplitude computed to all orders in the 't Hooft coupling is not renormalised! It is a unique situation in a quantum field theory that the scattering amplitude doesn't receive loop corrections. This indicates the presence of powerful symmetry structures within the theory. This also suggests that higher point amplitudes may be easier to compute using four point amplitudes as building blocks. These higher point amplitudes not only serve as a testing tool for duality but also a probe into the symmetry structure of the theory. As a first step towards this goal, we begin by computing arbitrary n point tree level amplitudes in the N=2 theory via BCFW recursion relations. We then show that the four point tree level amplitude enjoys a dual superconformal symmetry. Since the all loop four point amplitude is tree level exact, it follows that the dual superconformal symmetry is exact to all loops. This is in contrast to highly supersymmetric examples such as N=4 SYM and N=6 ABJM, where the dual superconformal symmetry is in general anomalous. Furthermore, we show that the superconformal and dual superconformal symmetries generate an infinite dimensional Yangian symmetry for the four point amplitude. If these symmetries persist to higher point amplitudes, this suggests that the N=2 superconformal Chern-Simons matter theory may be integrable.
Chern-Simons theories coupled to fundamental matter have a wide variety of applications ranging from Quantum Hall effect to Quantum gravity via AdS/CFT. These theories enjoy a strong weak duality that has been tested to a very good accuracy via large N computations, such as thermal partition functions, and S matrices. Supersymmetric Chern-Simons theories are equally interesting since they have a self duality and relate to non-supersymmetric theories via RG flows. In the N=2,3 supersymmetric Chern-Simons matter theories, the four point amplitude computed to all orders in the 't Hooft coupling is not renormalised! It is a unique situation in a quantum field theory that the scattering amplitude doesn't receive loop corrections. This indicates the presence of powerful symmetry structures within the theory. This also suggests that higher point amplitudes may be easier to compute using four point amplitudes as building blocks. These higher point amplitudes not only serve as a testing tool for duality but also a probe into the symmetry structure of the theory. As a first step towards this goal, we begin by computing arbitrary n point tree level amplitudes in the N=2 theory via BCFW recursion relations. We then show that the four point tree level amplitude enjoys a dual superconformal symmetry. Since the all loop four point amplitude is tree level exact, it follows that the dual superconformal symmetry is exact to all loops. This is in contrast to highly supersymmetric examples such as N=4 SYM and N=6 ABJM, where the dual superconformal symmetry is in general anomalous. Furthermore, we show that the superconformal and dual superconformal symmetries generate an infinite dimensional Yangian symmetry for the four point amplitude. If these symmetries persist to higher point amplitudes, this suggests that the N=2 superconformal Chern-Simons matter theory may be integrable.
Posted by: IC
Thu
20 Sep 2018
Entanglement branes in a two-dimensional string theory
Gabriel Wong
(Fudan U)
Abstract:
What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the Modular hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an E-brane.
What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the Modular hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an E-brane.
Posted by: QMW
Thu
13 Sep 2018
Central charge of self-dual strings from holography
Ronnie Rodgers
(Southampton U.)
Abstract:
M-theory is a candidate for a theory of quantum gravity. Its fundamental objects are called M2-branes and M5-branes. The low-energy theory describing coincident M5-branes is poorly understood in many respects, with holography providing one of the most useful tools to further that understanding. It is known that the theory should possess solitonic solutions called "self-dual strings". An important quantity characterising these strings is their central charge, which among other things counts the massless degrees of freedom on the string. I will describe configurations of M-branes dual to the insertion of infinite tension self-dual strings into the M5-brane theory, and how calculation of holographic entanglement entropy in such set-ups yields the central charge of the self-dual string.
M-theory is a candidate for a theory of quantum gravity. Its fundamental objects are called M2-branes and M5-branes. The low-energy theory describing coincident M5-branes is poorly understood in many respects, with holography providing one of the most useful tools to further that understanding. It is known that the theory should possess solitonic solutions called "self-dual strings". An important quantity characterising these strings is their central charge, which among other things counts the massless degrees of freedom on the string. I will describe configurations of M-branes dual to the insertion of infinite tension self-dual strings into the M5-brane theory, and how calculation of holographic entanglement entropy in such set-ups yields the central charge of the self-dual string.
Posted by: QMW