I show that an analog of the crossed product construction that takes type 𝐼𝐼𝐼1 algebras to type 𝐼𝐼 algebras exists also in the type 𝐼 case. This is particularly natural when the local algebra is a non-trivial direct sum of type 𝐼 factors. Concretely, I rewrite the usual type 𝐼 trace in a different way and renormalise it. This new renormalised trace stays well-defined even when each factor is taken to be type 𝐼𝐼𝐼. I am able to recover both type 𝐼𝐼 ∞  as well as type 𝐼𝐼1 algebras by imposing different constraints on the central operator in the code. An example of this structure appears in holographic quantum error-correcting codes; the central operator is then the area operator.

United Kingdom

Ronak Soni

A type I approximation of the crossed product

We study how entanglement spreads in the boundary duals of finite-cutoff three-dimensional theories with positive, negative and zero cosmological constant, the   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  + Λ2 two-dimensional theories. We first study the Hawking-Page transition in all three cases, and find that there is a transition in all three scenarios at the temperature where the lengths of the two cycles of the torus are the same. We then study the entanglement entropy in the thermofield double states above the Hawking-Page transition, of regions symmetrically placed on the two boundaries. We consider the case where the region is one interval on each side, and the case where it is two intervals on each side. We give an entanglement tsunami interpretation of the time-evolution of the entanglement entropies.

United States

Evan Coleman

Sungyeon Yang

On the spread of entanglement at finite cutoff

We obtain microstates accounting for the Gibbons-Hawking entropy in dS 3, along with a subleading logarithmic correction, from the solvable T   <math> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \overline{T} $$  + Λ2 deformation of a seed CFT with sparse light spectrum. The microstates arise as the dressed CFT states near dimension ∆ = c/6, associated with the Hawking-Page transition; they dominate the real spectrum of the deformed theory. We exhibit an analogue of the Hawking-Page transition in de Sitter. Appropriate generalizations of the T   <math> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \overline{T} $$  + Λ2 deformation are required to treat model-dependent local bulk physics (subleading at large central charge) and higher dimensions. These results add considerably to the already strong motivation for the continued pursuit of such generalizations along with a more complete characterization of T   <math> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \overline{T} $$  type theories, building from existing results in these directions.

Edward Mazenc

Vasudev Shyam

Eva Silverstein

Argentina

Gonzalo Torroba

De Sitter microstates from T   <math> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \overline{T} $$  + Λ2 and the Hawking-Page transition

We study the Page curve and the island rule for black holes evaporating into gravitating baths, with an eye towards establishing a connection with the ER=EPR proposal. We consider several models of two entangled 2d black holes in Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first, “doubled PSSY,” model is one in which the black holes have end-of-the-world (ETW) branes with a flavour degree of freedom. We study highly entangled states of this flavour degree of freedom and find an entanglement-induced Hawking-Page-like transition from a geometry with two disconnected black holes to one with a pair of black holes connected by a wormhole, thus realising the ER = EPR proposal. The second model is a dynamical one in which the ETW branes do not have internal degrees of freedom but the JT gravity is coupled to a 2d CFT, and we entangle the black holes by coupling the two CFTs at the AdS boundary and evolving for a long time. We study the entanglement entropy between the two black holes and find that the story is substantially similar to that with a non-gravitating thermal bath. In the third model, we couple the two ends of a two-sided eternal black hole and evolve for a long time. Finally, we discuss the possibility of a Hawking-Page-like transition induced by real-time evolution that realises the ER = EPR proposal in this dynamical setting.

Louise Anderson

Onkar Parrikar

Islands with gravitating baths: towards ER = EPR

We study the problem of revealing the entanglement wedge using simple operations. We ask what operation a semiclassical observer can do to bring the entanglement wedge into causal contact with the boundary, via backreaction.

Adam Levine

Arvin Shahbazi-Moghaddam

Seeing the entanglement wedge

We recast the joint   <math> <mi>J</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ J\overline{T} $$ ,   <math> <mi>T</mi> <mover> <mi>J</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{J} $$  and   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformations as coupling the original theory to a mixture of topological gravity and gauge theory. This geometrizes the general flow triggered by irrelevant deformations built out of conserved currents and the stress-energy tensor, by means of a path integral kernel. The partition function of the deformed theory satisfies a diffusion-like flow equation similar to that found in the pure   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  case. Our proposal passes two stringent tests. Firstly, we recover the classical deformed actions from the kernel, reproducing the known expressions for the free boson and fermion. Secondly, we explicitly compute the torus path integral along the flow and show it localizes to a finite-dimensional, one-loop exact integral over base space torus moduli. The dressed energy levels so obtained match exactly onto those previously reported in the literature.

Jeremías Aguilera-Damia

Victor Giraldo-Rivera

Ignacio Landea

A path integral realization of joint   <math> <mi>J</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ J\overline{T} $$ ,   <math> <mi>T</mi> <mover> <mi>J</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{J} $$  and   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  flows

A definition for the entanglement entropy in both Abelian and non-Abelian gauge theories has been given in the literature, based on an extended Hilbert space construction. The result can be expressed as a sum of two terms, a classical term and a quantum term. It has been argued that only the quantum term is extractable through the processes of quantum distillation and dilution. Here we consider gauge theories in the continuum limit and argue that quite generically, the classical piece is dominated by modes with very high momentum, of order the cut-off, in the direction normal to the entangling surface. As a result, we find that the classical term does not contribute to the relative entropy or the mutual information, in the continuum limit, for states which only carry a finite amount of energy above the ground state. We extend these considerations for p-form theories, and also discuss some aspects pertaining to electric-magnetic duality.

India

Upamanyu Moitra

Sandip Trivedi

Entanglement entropy, relative entropy and duality

We describe an algorithmic method to calculate the   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$  deformed Lagrangian of a given seed theory by solving an algebraic system of equations. This method is derived from the topological gravity formulation of the deformation. This algorithm is far simpler than the direct partial differential equations needed in most earlier proposals. We present several examples, including the deformed Lagrangian of (1,1) supersymmetry. We show that this Lagrangian is off-shell invariant through order λ2 in the deformation parameter and verify its SUSY algebra through order λ.

Jeremias Aguilera-Damia

Daniel Freedman

<math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$ -deformed actions and (1,1) supersymmetry

In recent years soft factorization theorems in scattering amplitudes have been reinterpreted as conservation laws of asymptotic charges. In gauge, gravity, and higher spin theories the asymptotic charges can be understood as canonical generators of large gauge symmetries. Such a symmetry interpretation has been so far missing for scalar soft theorems. We remedy this situation by treating the massless scalar field in terms of a dual two-form gauge field. We show that the asymptotic charges associated to the scalar soft theorem can be understood as generators of large gauge transformations of the dual two-form field.

Uruguay

Miguel Campiglia

Canada

Laurent Freidel

Florian Hopfmueller

Scalar asymptotic charges and dual large gauge transformations

We analyse the dynamics of near-extremal Reissner-Nordström black holes in asymptotically four-dimensional Anti de Sitter space (AdS4). We work in the spherically symmetric approximation and study the thermodynamics and the response to a probe scalar field. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the SYK model. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.

Pranjal Nayak

Ashish Shukla

V. Vishal

On the dynamics of near-extremal black holes