ICTS

TBA

In this talk, I will give a summary of our series of works on time evolutions of entanglement entropy for locally excited states in 2d CFTs. We will show that the behaviors change drastically depending on the nature of CFTs, whether they are rational, irrational or chaotic. We present our latest results based on Zamolodchikov's recursion relations. We will also discuss higher dimensional results.

In order to elucidate the recent tantalizing hints at a holographic connection between bulk geometry and boundary entanglement, we explore the nature of geometric proofs of entanglement relations. In particular, we use the bit thread formulation of holographic entanglement entropy to highlight the distinction between strong subadditivity and monogamy of mutual information, arguing that the latter is more deeply rooted in bulk locality.

In this talk we shall start with some exact computation large N computation of scattering amplitude in CS matter theories. We'll then discuss how to understand some the results based on symmetry principle such as Dual conformal invariance. Then concentrate on higher point scattering amplitude and discuss BCFW recursion relations to compute higher point tree level amplitude. We then discuss some facts about loop level 6 and higher point scattering amplitudes.

We will review the Sachdev Ye Kitaev model and describe how it shares some features with nearly extremal black holes.
We also describe the dynamics of nearly extremal black holes.
We will go over different physical phenomena, including chaos, quantum teleportation, etc, and their common manifestation in these two systems.

We construct a bulk dual to the pseudo Nambu Goldstone sector of the SYK model by performing a KK reduction of Einstein gravity in asymptotically AdS(3) geometry.
The KK reduction leads to a Jackiw-Teitelbom theory; the dilaton is identified with the radius of the KK circle. The construction can be extended to Einstein-U(1) Chern-Simons theory whose KK reduction leads to Jackiw-Teitelboim-BF theory. The large gauge transformations of this theory get identified with the Nambu-Goldstone modes of the charged SYK model. The bulk dual correctly reproduces the effective action of these modes, consisting of the Schwarzian and a sigma-model term, as found in Davison et al (hep-th/1612.00849).

W symmetry underlies the AdS3/CFT2 correspondence with higher spin symmetry. There exists a useful triangle connecting W symmetry, affine Yangian, and plane partition representations. Further, this triangle can serve as the building block of new VOA's and affine Yangians. As an example, I will explain how to construct the N=2 version of this triangle, which gives rise to a new type of affine Yangian and its twin-plane partition representations.

We will review the Sachdev Ye Kitaev model and describe how it shares some features with nearly extremal black holes.
We also describe the dynamics of nearly extremal black holes.
We will go over different physical phenomena, including chaos, quantum teleportation, etc, and their common manifestation in these two systems.

I will discuss the question of what is the geometry dual to a typical black hole microstate in AdS/CFT and how the region behind the horizon may be probed by using time-dependent perturbations of the CFT Hamiltonian.

After a brief review, I will discuss how a new formulation of a low energy Schwinger Keldysh effective action gives rise to the appearance of an entropy current, Onsager relations, and further constraints on hydrodynamics which are not implied by the either

We explore the viability of fuzzballs as candidate microstate geometries for the black hole, and their possible role in resolutions of the information paradox. We argue that if fuzzballs provide a description of black-hole microstates, then the typical fuzzball geometry can only differ significantly from the conventional black-hole geometry at a Planck-scale-distance from the horizon. However, precisely in this region, quantum fluctuations in the fuzzball geometry become large and the fuzzball geometry becomes unreliable. We verify these expectations through a detailed calculation of quantum expectation values and quantum fluctuations in the two-charge fuzzball geometries. We then examine some of the solutions discovered in arXiv:1607.03908. We show, based on a calculation of a probe two-point function in this background, that these solutions, and others in their class, violate robust expectations about the gap in energies between successive energy eigenstates, and differ too much from the conventional black hole to represent viable microstates. We conclude that while fuzzballs are interesting star-like solutions in string theory, they do not appear to be relevant for resolving the information paradox, and cannot be used to make valid inferences about black-hole interiors.

Operator spreading refers to the growth of local operators in spatial support and complexity under unitary dynamics. I will discuss some exact results on operator spreading under local random unitary circuits, how they tie into more general beliefs about how operators spread in different settings, and finally how these beliefs constrain the phase space for finding examples of time translation symmetry breaking.

I will describe recent advancements which results in a way to reconstruct perturbative bulk physics purely from the CFT data. I will also discuss possible implications for constructing a bulk quantum gravity theory.

In the first part of the talk I will discuss a proposal for the CFT dual of string theory on AdS3 x S3 x S3 x S1. The proposed dual satisfies a number of non-trivial consistency conditions; in particular it matches the BPS spectrum of supergravity that we also determined from first principles. In the second half of the talk, I will explain how the higher spin symmetry of string theory on AdS3 at the tensionless point can be directly understood from a world-sheet perspective.

It has been conjectured that fermions minimally coupled to a Chern- Simons gauge eld de ne a conformal eld theory (CFT) that is level-rank dual to Chern-Simons gauged Wilson-Fisher Bosons. The CFTs in question admit relevant deformations parametrized by a real mass. When the mass deformation is positive, the duality of the two deformed theories has previously been checked in detail in the large N limit by comparing explicit all orders results on both sides of the duality. In this paper we perform a similar check for the case of negative mass deformations. In this case the bosonic eld condenses triggering the Higgs mechanism. The effective excitations in this phase are massive W bosons. By summing all leading large N graphs involving these W bosons we nd an all orders (in the 't Hooft coupling) result for the thermal free energy of the bosonic theory in the condensed phase. Our final answer perfectly matches the previously obtained fermionic free energy under the conjectured duality map.

Dispersion relations, often called Kramers-Kronig relations, exploit causality to reconstruct the real part of a scattering amplitude from its imaginary (or absorptive) part, which is often easier to measure or compute. In the context of strongly coupled conformal theories, a similar formula reconstructs correlators from essentially kinematical information about a few light operators in the spectrum. I will illustrate in examples how this automatically produces the correlators of a local AdS theory, as a consequence of unitarity of the CFT (positivity of the absorptive part).

Since this conference is about 20 years of ads/cft I will review some aspects of black holes in ads/cft and also describe some recent work.

TBA

Bit threads offer a novel perspective on holographic entanglement entropy. Using tools from network theory, specifically the concept of multicommodity flows, we will use bit threads to prove the “monogamy of mutual information” property of holographic entanglement entropies. The proof will lead to a conjecture about the general entanglement structure of holographic states.

I argue that the space of not necessarily unitary conformal field theories with abelian symmetry forms a vector space over complex numbers. This is done by formulating the CFT consistency condition as factorization of the n-point functions of a certain chosen operator.

After describing the basics of the conformal bootstrap, based on Polyakov's crossing symmetric approach, formulated in Mellin space, we outline some of the simplifications in this approach. We also discuss the issue of contact Witten diagrams in mellin space and their role. 

We derive two constraints on conformal field theories in 3 and 2 dimensions. The constraints indicate that they arise from unitarity however the derivation does not directly use this property. Finally we examine the chaos bound for conformal field theories in 2 dimensions and show that the bound is violated when the OTO is evaluated on a state which large negative conformal dimensions.

A new class of higher-spin gauge theories associated with various Coxeter groups will be proposed. The emphasize is on the $B_p$--models. The multi-particle $B_2$--higher-spin theory is conjectured to be associated with String Theory. $B_p$--higher-spin models with $p>2$ are anticipated to be dual to the rank-$p$ boundary tensor sigma-models. $B_p$ higher-spin models with $p\geq 2$ possess two coupling constants responsible for higher-spin interactions in $AdS$ background and stringy/tensor effects, respectively. Consistency of the holographic interpretation of the boundary matrix-like model in the $B_2$-HS model will be shown to demand $N\geq 4$ SUSY, suggesting duality with the $N=4$ SYM upon spontaneous breaking of HS symmetries.

Tensor models define a new large $N$ limit dominated by melonic diagrams. While it seems unlikely that theories with melonic dominance make sense in dimensions greater than $1$, it seems important to confirm this by carefully exploring the range of possibilities for melonic CFT’s, and their relationships to simpler large $N$ theories based on vector or matrix degrees of freedom. In this context we will review some of the work on fermionic and bosonic tensor models in $d$ dimensions over the last year. One positive outcome of these explorations is that it appears possible to study fermionic tensor models in $1$ dimension at finite $N$ via an epsilon expansion, starting from $2-\epsilon$ dimensions.

Tree level scattering amplitudes in gauge theories and gravity satisfy an infinity of factorization theorems. Building on prior work of Strominger et al, we show that all the factorization theorems can be understood as Ward identities which are associated to an infinity Hierarchy of conserved charges in the classical theory.  This is work in progress with Miguel Campiglia.

TBA