Modular Hamiltonians in flat holography and (W)AdS/WCFT

TL;DR

This paper explores holographic entanglement and modular Hamiltonians in non-AdS holographic models, specifically flat$_3$/BMSFT and (W)AdS$_3$/WCFT, revealing new insights into boundary theories with infinite symmetries.

Contribution

It derives the modular Hamiltonian for single intervals in BMSFTs and WCFTs and identifies their holographic duals, extending entanglement entropy laws to non-AdS holography.

Findings

Derived modular Hamiltonians for BMSFTs and WCFTs.

Identified holographic duals in the bulk for these theories.

Extended the first law of entanglement entropy to non-AdS models.

Abstract

We study several aspects of holographic entanglement in two models known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. These are two examples of holography beyond AdS/CFT where the the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS$_3$ or AdS$_3$ backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on "modular chaos" introduced recently in the context of the AdS/CFT correspondence.