$T \bar T$ and EE, with implications for (A)dS subregion encodings

TL;DR

This paper explores how $T ar T$ deformations affect subregion dualities, entropy, and bulk point encoding in holographic theories, revealing new behaviors and nonlocality features in deformed AdS and dS spacetimes.

Contribution

It introduces new calculations of entanglement entropy in deformed holographic theories and analyzes the structure of operator algebras and subregion dualities under $T ar T$ deformations.

Findings

Agreement between gravity and deformed-CFT results at large central charge.

Deformed causal and entanglement wedges exhibit new behaviors, such as the causal wedge exceeding the entanglement wedge.

Evidence of nonlocality similar to string theory in boosted regions.

Abstract

We initiate a study of subregion dualities, entropy, and redundant encoding of bulk points in holographic theories deformed by $T \bar T$ and its generalizations. This includes both cut off versions of Anti de Sitter spacetime, as well as the generalization to bulk de Sitter spacetime, for which we introduce two additional examples capturing different patches of the bulk and incorporating the second branch of the square root dressed energy formula. We provide new calculations of entanglement entropy (EE) for more general divisions of the system than the symmetric ones previously available. We find precise agreement between the gravity side and deformed-CFT side results to all orders in the deformation parameter at large central charge. An analysis of the fate of strong subadditivity for relatively boosted regions indicates nonlocality reminiscent of string theory. We introduce the structure of operator algebras in these systems. The causal and entanglement wedges generalize to appropriate deformed theories but exhibit qualitatively new behaviors, e.g. the causal wedge may exceed the entanglement wedge. This leads to subtleties which we express in terms of the Hamiltonian and modular Hamiltonian evolution. Finally, we exhibit redundant encoding of bulk points, including the cosmological case.