**Collection Number**S003

**Collection Type**Series

## Towards Recovering a Holographic Bulk from Entanglement

The AdS/CFT correspondence provides a remarkably useful tool

for asking questions in quantum gravity, as it formulates a theory of

quantum gravity in terms of an ordinary non-gravitational quantum field

theory. Fruitfully exploiting this correspondence therefore requires

understanding how to translate the language of CFT into gravity; a key

insight that has emerged over the past decade is that the entanglement

structure of the CFT must be intimately tied to the emergence of the

## Strings on the Keldysh Contour

There is a fundamental tension between what string theory computes (S-matrix elements) and what you can compute in QFT on a time-dependent backgrounds (real time operator expectation values). The prescription for computing time dependent expectation values in QFT involves a path integral defined on a closed time path, known as the Keldysh contour. In this talk, we'll discuss how a worldsheet formulation of string theory must perceive the Keldysh contour and how this modifies critical string theory at tree level in the string coupling.

## The holographic dual of Renyi relative entropy

The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for all CFT’s. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an auxiliary AdS-Rindler spacetime.

## Stringy ER=EPR

I will describe an example in which ER=EPR can be understood as a worldsheet string duality, by finding the Lorentzian continuation of the FZZ duality. The result is that string perturbation theory around the thermofield double state in a disconnected spacetime with a condensate of entangled folded strings is equivalent to string theory in a connected two sided black hole spacetime. Important ingredients are the Lorentzian interpretation of time winding vertex operators, and string theory with target space Schwinger-Keldysh contours.

## Holographic correlators from bootstrap and supersymmetric localization

In this talk, I will describe some of the recent progress on computing holographic correlators using analytic bootstrap techniques combined with supersymmetric localization. From taking a certain flat space limit of the holographic correlators, one can obtain scattering amplitudes of gravitons in string theory, and one can then reproduce some of the known results for these scattering amplitudes. I will focus mostly on the case of the 4d {\cal N} = 4 super-Yang-Mills theory, but I will also mention related work in the 3d ABJM theory.

## Implications of the ANEC in four dimensional SCFTs

The averaged null energy condition (ANEC) can be used to put constraints on the scaling dimensions of operators in a local CFTs. In some cases these are stronger than the unitarity bounds. I will consider four dimensional N=1 superconformal field theories (SCFTs) and discuss bounds on generic long and protected multiplets with spin (j,0). Some of them can be obtained analytically and others can be studied by means of a simple semidefinite programming problem. I will also briefly mention the consequences for N=2,4 SCFTs. Based on [1905.09293].

## Black hole microstate cosmology

## Dynamical constraints on RG flows and cosmology

In QFT, the renormalization group is usually formulated in Euclidean signature. I will discuss time-dependent probes of the RG, in Lorentzian signature, and derive new dynamical constraints that govern the spread of local operators. Through a chain of Wick rotations and dualities, the same methods lead to new sum rules for inflationary correlators, which relate observable quantities like the inflationary speed of sound to properties of the UV.

## Geometric Extremization for AdS/CFT and Black Hole Entropy

We consider supersymmetric $AdS_3\times Y_7$ solutions of type IIB supergravity dual to N=(0,2) SCFTs in d=2, as well as $AdS_2\times Y_9$ solutions of D=11 supergravity dual to N=2 supersymmetric quantum mechanics, some of which arise as the near horizon limit of supersymmetric, charged black hole solutions in $AdS_4$. The relevant geometry on $Y_{2n+1}$, $n\ge 3$ was first identified in 2005-2007 and around that time infinite classes of explicit examples solutions were also found but, surprisingly, there was little progress in identifying the dual SCFTs.

## Locality or non-locality? Fermionic entanglement on the torus

Understanding entanglement in QFTs is a challenging topic that involves many aspects. One important probe for this is the modular (or entanglement) Hamiltonian, which is closely related to the Unruh effect. We determine this operator for the chiral fermion at finite temperature on the circle using complex analysis, and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality as a function of temperature, thus bridging the gap between previously known limits.