Title: "K3 Elliptic genus and an umbral moonshine module"

Abstract: I will talk about an umbral moonshine module that we recently constructed with Miranda and S. Harrison (arxiv:1709.01952), and how it is related to the elliptic genus of K3 surfaces. While going through the basics of this construction, I will also review certain aspects of both umbral and Conway moonshine.

Title: Universal counting of black hole microstates and supersymmetric localization

Abstract: Any SCFT with a continuous R-symmetry contains a sector which is “closed” under RG flow. In the case of 3d theories, I will explain how combining this observation with holography and supersymmetric localization leads to the microscopic counting of entropy for an infinite class of AdS_4 back holes.

Time permitting, I will argue that the same set of ideas leads to various nontrivial relations among seemingly unrelated matrix models at large N and discuss the relation to microstate counting of black p-branes.

Conformal field theories with flavor symmetries admit a limit where one zooms in on the spectrum of the dilatation operator close to a unitarity bound of the form D=J where D is the conformal dimension and J is some U(1) charge.

I will consider N=4 SU(N) SYM close to the unitarity bound D=J with J=J_1+J_2 where J_1 and J_2 are two of the 3 R-charges. This is known as the SU(2) sector. There exists a decoupling limit in which the 't Hooft coupling \lambda is sent to zero while (D-J)/\lambda is kept fixed. For large J the limit theory is the Landau-Lifshitz sigma model which is the continuum limit of the Heisenberg spin chain (the 1-loop dilatation operator in the SU(2) sector).

I will show that this decoupling limit can also be taken on the string theory side of the correspondence and that it leads to new non-relativistic string theories describing string propagation in Newton-Cartan-type target spaces.

This talk is based on 0806.3370 and 1705.03535.

November 16: Gerben Oling

Title: Radial Newton-Cartan from AdS3/CFT2

Abstract: It is often not clear how a given relativistic theory can be obtained as a limit of a relativistic one. For example in gravity, distinguishing a time direction in local frames means using Newton-Cartan geometry instead of Riemannian geometry, and these are not obviously related. However, it was recently found that just like Einstein gravity, particular nonrelativistic theories of gravity can be formulated as Chern-Simons theories in three dimensions. We leverage this connection to explicitly implement a non-relativistic limit that maps not only the local and asymptotic symmetry algebra, but identifies the full phase space. Remarkably, the resulting Newton-Cartan theory is foliated along the radialdirection. This is work to appear soon with Jelle Hartong, Yang Lei and Niels Obers.

November 10: Faculty corner - Miranda Cheng

Title: M-theory, 3-manifolds and the zoo of modular freaks

Abstract: In my talk I will describe certain new (and partially conjectural) relations between 3-manifold quantum invariants and specific representations of SL(2,Z), inspired by the 3d-3d correspondence and realised by mock, false, and quantum modular forms. The talk will be based on ongoing adventure with Francesca Ferrari, Sergei Gukov and Sarah Harrison.

Title: Extremal CFTs with small central charge Abstract: In the talk I will review the different properties of 2d extremal chiral (super)conformal field theories with central charge smaller or equal to 24. These are theories whose only operators with dimension smaller or equal to c/24 are the vacuum and its Virasoro descendents. One of the most famous example is the Monster CFT. Its twining functions can be completely constructed from the vacuum structure and the modular properties of the functions via a Rademacher sum (Farey tail). Following a work in progress with Sarah Harrison, I will investigate the extent to which such a property, holds for other known extremal theories.

October 20: William Cottrell

Title: Complexity Is Simple!

Abstract: In this talk we investigate the role of Lloyd's computational bound in holographic complexity. Our goal is to translate the assumptions behind Lloyd's proof into the bulk language. In particular, we discuss the distinction between orthogonalizing and `simple' gates and argue that these notions are useful for diagnosing holographic complexity. We show that large black holes constructed from series circuits necessarily employ simple gates, and thus do not satisfy Lloyd's assumptions. We also estimate the degree of parallel processing required in this case for elementary gates to orthogonalize. Finally, we show that for small black holes at fixed chemical potential, the orthogonalization condition is satisfied near the phase transition, supporting a possible argument for the Weak Gravity Conjecture first advocated in Brown et al.

Title: Universal features of self-dual string CFTs

Abstract: A large number of six-dimensional superconformal field theories (SCFTs) has been discovered since the 1990s, and recently a classification of all possible 6d SCFTs has been proposed in the context of F-theory. 6d SCFTs are characterized in terms of their spectrum of vector, hyper- and tensor multiplets, and a salient feature is the existence of strings that couple to the tensor multiplets. The strings’ dynamics are captured by interacting 2d CFTs. Understanding these 2d CFTs (as well as the 2d CFTs that describe bound states of strings) is an interesting problem, since their elliptic genera encode various important properties of the 6d SCFTs such as their superconformal index and other supersymmetric partition functions. While the gauge and global symmetries vary widely between different 6d SCFTs, in this talk I will argue that the 2d CFTs describing their strings all have a common structure, which strongly constrains the form of the strings’ elliptic genera, and in many (if not all) cases is powerful enough to uniquely determine them.

Abstract: I will discuss recent work on entanglement renormalization schemes that rigorously approximate the correlation functions of simple (free) theories. If time permits, I will also give a brief progress report on tensor network toy models of holography. September 22: Alex Belin

Title: Quantum corrections to holographic entanglement entropy

Abstract: The RT proposal associates the entanglement entropy of a boundary region with the area of a minimal surface in the bulk. This statement is to hold at leading order in the 1/N expansion. FLM and JLMS made proposals on how to deal with the subleading order: it involves computing the bulk entanglement entropy through the RT surface. In this talk, I will shortly review these proposals and test them in the context of the AdS_3/CFT_2 duality, by considering excited states of the CFT. This talk will be based on work in progress with N. Iqbal and S. Lokhande.

Abstract: In this journal club I will present unpublished work with Ted Jacobson (to appear soon) on causal diamonds in (A)dS. We employ the unique conformal isometry that preserves causal diamonds associated to spherical regions in pure (A)dS to derive thermodynamic relations. The conformal Killing vector field that generates this conformal isometry can be explicitly computed and automatically gives rise to a zeroth law. Furthermore, we derive a first law of causal diamond mechanics for general relativity by applying Wald’s variational identity to the geometric setting. In addition to the standard area variation the classical first law contains a volume variation. In my talk I will mention several interesting limiting cases of the first law, such as cosmological horizons, (AdS-)Rindler horizons, small diamonds and the Wheeler-de Witt patch in AdS. Finally, if time permits, I will speculate about possible microscopic interpretations of the first law.

Abstract: Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some surprising similarities. (1707.08570)

Abstract: In this Journal club I present a paper that will appear soon. In this paper I address an old problem in the physics of black holes: how does black hole entropy know about U-duality symmetry of string theory? We know that the area formula respects that symmetry: black hole solutions in different U-duality frames have the same area formula. But what about the quantum corrections? To answer this question we have to address the problem at the non-perturbative level. I will show how non-perturbative dualities of string theory on AdS_2 are related to complicated identities of Kloosterman sums known as Sums of Kloosterman Sums. The lesson to take home is the connection between non-perturbative effects in AdS quantum gravity and arithmetic properties of whole numbers.

Fall 2017December 15:Vassilis AnagiannisTitle: "K3 Elliptic genus and an umbral moonshine module"Abstract: I will talk about an umbral moonshine module that we recently constructed with Miranda and S. Harrison (arxiv:1709.01952), and how it is related to the elliptic genus of K3 surfaces. While going through the basics of this construction, I will also review certain aspects of both umbral and Conway moonshine.Papers to discuss in the last JC of the year:

1- The AdS3 Propagator and the Fate of Locality , Fitzpatrick et al

2- Probing beyond ETH at large c , Faulkner et al

3- Higher genus Siegel forms and multi-center black holes in N=4 supersymmetric string theory(Denef et al)

4- Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space(Cao, Carroll)

5- Quantum Gates to other Universes (Bachas, Lavdas)

6- Homogeneous Nonrelativistic Geometries as Coset Spaces (Jelle et al)

December 1:Marcos CrichignoTitle: Universal counting of black hole microstates and supersymmetric localizationAbstract: Any SCFT with a continuous R-symmetry contains a sector which is “closed” under RG flow. In the case of 3d theories, I will explain how combining this observation with holography and supersymmetric localization leads to the microscopic counting of entropy for an infinite class of AdS_4 back holes.Time permitting, I will argue that the same set of ideas leads to various nontrivial relations among seemingly unrelated matrix models at large N and discuss the relation to microstate counting of black p-branes.

and we discussed:

1- An integrable Lorentz-breaking deformation of two-dimensional CFTs (Monica Guica)

2- Topology in time-reversal symmetric crystals (de drie J's)

3- Background independence of closed superstring field theory(Ashoke Sen)

4- A Non-Unitary Surprise (Buican & Laczko)

5- Higher Spin de Sitter Hilbert Space (Dio, et al.)

6-Hints towards the Emergent Nature of Gravity (Manus, et al.)

7- On the chiral algebra of Argyres-Douglas theories and S-duality (Choi & Nishinaka)

November 22:Jelle HartongTitle: Holography Close to a Unitarity BoundAbstract:Conformal field theories with flavor symmetries admit a limit where one zooms in on the spectrum of the dilatation operator close to a unitarity bound of the form D=J where D is the conformal dimension and J is some U(1) charge.

I will consider N=4 SU(N) SYM close to the unitarity bound D=J with J=J_1+J_2 where J_1 and J_2 are two of the 3 R-charges. This is known as the SU(2) sector. There exists a decoupling limit in which the 't Hooft coupling \lambda is sent to zero while (D-J)/\lambda is kept fixed. For large J the limit theory is the Landau-Lifshitz sigma model which is the continuum limit of the Heisenberg spin chain (the 1-loop dilatation operator in the SU(2) sector).

I will show that this decoupling limit can also be taken on the string theory side of the correspondence and that it leads to new non-relativistic string theories describing string propagation in Newton-Cartan-type target spaces.

This talk is based on 0806.3370 and 1705.03535.

November 16:Gerben OlingTitle: Radial Newton-Cartan from AdS3/CFT2Abstract: It is often not clear how a given relativistic theory can be obtained as a limit of a relativistic one. For example in gravity, distinguishing a time direction in local frames means using Newton-Cartan geometry instead of Riemannian geometry, and these are not obviously related. However, it was recently found that just like Einstein gravity, particular nonrelativistic theories of gravity can be formulated as Chern-Simons theories in three dimensions. We leverage this connection to explicitly implement a non-relativistic limit that maps not only the local and asymptotic symmetry algebra, but identifies the full phase space. Remarkably, the resulting Newton-Cartan theory is foliated along theradialdirection. This is work to appear soon with Jelle Hartong, Yang Lei and Niels Obers.November 10:Faculty corner - Miranda ChengTitle: M-theory, 3-manifolds and the zoo of modular freaksAbstract: In my talk I will describe certain new (and partially conjectural) relations between 3-manifold quantum invariants and specific representations of SL(2,Z), inspired by the 3d-3d correspondence and realised by mock, false, and quantum modular forms. The talk will be based on ongoing adventure with Francesca Ferrari, Sergei Gukov and Sarah Harrison.and we discussed:

2- ’t Hooft anomalies and boundaries (Jensen, Shaverin, Yarom)

3. Universality of Quantum Information in Chaotic CFTs(Dymarsky, Lashkari, Liu)

4. Stability and boundedness in AdS/CFT with double trace deformations II: Vector Fields (Billy, et al.)

5. A One-loop Test of Quantum Black Holes in Anti de Sitter Space (Liu, Pando Zayas, et al.)

6. The String Landscape, the Swampland, and the Missing Corner (Vafa, et al.)

October 25:Francesca FerrariTitle: Extremal CFTs with small central chargeAbstract: In the talk I will review the different properties of 2d extremal chiral (super)conformal field theories with central charge smaller or equal to 24. These are theories whose only operators with dimension smaller or equal to c/24 are the vacuum and its Virasoro descendents. One of the most famous example is the Monster CFT. Its twining functions can be completely constructed from the vacuum structure and the modular properties of the functions via a Rademacher sum (Farey tail). Following a work in progress with Sarah Harrison, I will investigate the extent to which such a property, holds for other known extremal theories.October 20:William CottrellTitle:

Complexity Is Simple!Abstract: In this talk we investigate the role of Lloyd's computational bound in holographic complexity. Our goal is to translate the assumptions behind Lloyd's proof into the bulk language. In particular, we discuss the distinction between orthogonalizing and `simple' gates and argue that these notions are useful for diagnosing holographic complexity. We show that large black holes constructed from series circuits necessarily employ simple gates, and thus do not satisfy Lloyd's assumptions. We also estimate the degree of parallel processing required in this case for elementary gates to orthogonalize. Finally, we show that for small black holes at fixed chemical potential, the orthogonalization condition is satisfied near the phase transition, supporting a possible argument for the Weak Gravity Conjecture first advocated in Brown et al.

and we will discuss:

0. Symmetry and Emergence (Edward Witten)

1. Efficient decoding for the Hayden-Preskill Protocol (Yoshida, Kitaev)

October 13:Guglielmo LockhartTitle:

Universal features of self-dual string CFTsAbstract: A large number of six-dimensional superconformal field theories (SCFTs) has been discovered since the 1990s, and recently a classification of all possible 6d SCFTs has been proposed in the context of F-theory. 6d SCFTs are characterized in terms of their spectrum of vector, hyper- and tensor multiplets, and a salient feature is the existence of strings that couple to the tensor multiplets. The strings’ dynamics are captured by interacting 2d CFTs. Understanding these 2d CFTs (as well as the 2d CFTs that describe bound states of strings) is an interesting problem, since their elliptic genera encode various important properties of the 6d SCFTs such as their superconformal index and other supersymmetric partition functions. While the gauge and global symmetries vary widely between different 6d SCFTs, in this talk I will argue that the 2d CFTs describing their strings all have a common structure, which strongly constrains the form of the strings’ elliptic genera, and in many (if not all) cases is powerful enough to uniquely determine them.

and we will informally discuss:

1. Detachable circles and temperature-inversion dualities for CFTd (Shaghoulian, Horowitz)

2. Symmetry breaking in holographic theories with Lifshitz scaling (Jelle, et. al.)

3. Asymptotic Charges Cannot Be Measured in Finite Time (Bousso, et al.)

4. Complexity is simple! (Billy and Miguel)

5. On chaos and hydrodynamics arXiv:1710.00921 (Grozdanov, Schalm, Scopelliti) and arXiv:1710:01005 (Lucas)

6. From 3d duality to 2d duality (Aharony, Razamat, Willett)

7. Anomalies involving the space of couplings and the Zamolodchikov metric (Tachikawa)

October 6:Speakers discussionSeptember 27:Michael WalterTitle:

Tensor networks & entanglement renormalizationAbstract: I will discuss recent work on entanglement renormalization schemes that rigorously approximate the correlation functions of simple

(free) theories. If time permits, I will also give a brief progress report on tensor network toy models of holography.

September 22:Alex BelinTitle:

Quantum corrections to holographic entanglement entropyAbstract: The RT proposal associates the entanglement entropy of a boundary region with the area of a minimal surface in the bulk. This statement is to hold at leading order in the 1/N expansion. FLM and JLMS made proposals on how to deal with the subleading order: it involves computing the bulk entanglement entropy through the RT surface. In this talk, I will shortly review these proposals and test them in the context of the AdS_3/CFT_2 duality, by considering excited states of the CFT. This talk will be based on work in progress with N. Iqbal and S. Lokhande.

and we will informally discuss:

1. 1709.02819 - One-Loop Holographic Weyl Anomaly in Six Dimensions (Liu, McPeak)

2. The String Worldsheet as the Holographic Dual of SYK State (Cai et.al.)

3.Detachable circles and temperature-inversion dualities for CFTd (Shaghoulian, Horowitz)

4. U-duality Invariant Quantum Entropy from Sums of Kloosterman Sums (Joao)

5. Stringy N=(2,2) holography for AdS3 (Datta, Eberhardt, Gaberdiel)

6. Supersymmetry Breaking by Fluxes (Sethi)

September 15:Manus VisserTitle:

Thermodynamics of Causal Diamonds in (A)dSAbstract: In this journal club I will present unpublished work with Ted Jacobson (to appear soon) on causal diamonds in (A)dS. We employ the unique conformal isometry that preserves causal diamonds associated to spherical regions in pure (A)dS to derive thermodynamic relations. The conformal Killing vector field that generates this conformal isometry can be explicitly computed and automatically gives rise to a zeroth law. Furthermore, we derive a first law of causal diamond mechanics for general relativity by applying Wald’s variational identity to the geometric setting. In addition to the standard area variation the classical first law contains a volume variation. In my talk I will mention several interesting limiting cases of the first law, such as cosmological horizons, (AdS-)Rindler horizons, small diamonds and the Wheeler-de Witt patch in AdS. Finally, if time permits, I will speculate about possible microscopic interpretations of the first law.

and we will informally discuss:

1. 1709.01952 - K3 Elliptic genus and an umbral moonshine ( Anagiannis, Cheng, Harrison )

2. 1708.04242 - Monstrous entanglement ( Das, Datta, Pal )

3. 1709.03597 - Shockwaves from OPEs ( Afkhami-Jeddi, Hartman, Kundu, Tajdini )

4. 1709.01749 - On non-supersymmetric conformal manifolds: field theory and holography (Bashmakov, Bertolini & Raj) and 1709.03967 - Conformal manifolds: ODEs from OPEs (Behan)

5. Quantum Gates to other Universes (Bachas, Lavdas)

September 8:Ro JeffersonTitle:

Circuit complexity in QFTAbstract: Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some surprising similarities. (1707.08570)

and we will informally discuss:

1- Dear Qubitzers, GR=QM (L. Susskind)

2- 1709.01533 and 1708.08815

3- 1709.01052and 1708.09493

4- 1709.00445

September 1:Joao GomesTitle:

How Holography knows about U-dualityAbstract: In this Journal club I present a paper that will appear soon. In this paper I address an old problem in the physics of black holes: how does black hole entropy know about U-duality symmetry of string theory? We know that the area formula respects that symmetry: black hole solutions in different U-duality frames have the same area formula. But what about the quantum corrections? To answer this question we have to address the problem at the non-perturbative level. I will show how non-perturbative dualities of string theory on AdS_2 are related to complicated identities of Kloosterman sums known as Sums of Kloosterman Sums. The lesson to take home is the connection between non-perturbative effects in AdS quantum gravity and arithmetic properties of whole numbers.

Please vote for your favourite papers to be discussed on

https://goo.gl/forms/G7q9GxKLjfyfT6ew1