Cluster algebraic description of entanglement patterns for the BTZ black hole

2021/08/24 by Bercel Boldis, Péter Lévay
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1103/physrevd.105.046020

15 pages, 9 figures, LaTex

arxiv created 2021/08/24 · arxiv updated 2022/03/14

Abstract

We study the thermal state of a two dimensional conformal field theory which is dual to the static BTZ black hole in the high temperature limit. After partitioning the boundary of the static BTZ slice into N subsystems we show that there is an underlying C_N-1 cluster algebra encoding entanglement patterns of the thermal state. We also demonstrate that the polytope encapsulating such patterns in a geometric manner for a fixed N is the cyclohedron \mathcal C_N-1. Alternatively these patterns of entanglement can be represented in the space of geodesics (kinematic space) in terms of a Zamolodchikov Y-system of C_N-1 type. The boundary condition for such an Y-system is featuring the entropy of the BTZ black hole.

Cited by

• Notes on the double Wick rotated BTZ black hole