The Flat-Space Limit of AdS Coupled to a Bath

TL;DR

This paper develops a method to derive flat-space physics from AdS models coupled to a bath, revealing how boundary symmetries contract and analyzing entanglement entropy and black hole evaporation in the flat-space limit.

Contribution

It introduces a triple-scaling limit for AdS coupled to a bath, showing how boundary symmetries contract to flat space symmetries and analyzing entanglement entropy in this limit.

Findings

Flat-space limit reduces BCFT symmetry algebra via Wigner-In"on"u contraction.

Two notions of entanglement entropy lead to different Page curves.

Page time remains finite in 2D but diverges in higher dimensions.

Abstract

We explain how to take a well-defined flat-space limit of brane models of AdS coupled to a non-gravitating bath. In the dual BCFT this amounts to a triple-scaling limit where both the number of boundary degrees of freedom and the boundary coupling are taken to infinity while the BCFT boundary piecewise approaches a lightcone. We show how this procedure acts on the conformal generators as a Wigner-\.In\"on\"u contraction, reducing the global BCFT symmetry algebra to the global symmetry algebra of flat space. We discuss two natural notions of entanglement entropy of the flat-space dual. These are distinguished by whether modes that have left through $\mathcal I^\pm$ are included or not and give rise to a vanishing and non-trivial Page curve, respectively. Taking the flat-space limit of topological black holes we show that the Page time remains finite in two-dimensions. In $d > 2$ the Page time diverges in the flat limit, since AdS topological black holes become flat-space Rindler horizons.