Cluster algebraic description of entanglement patterns for the BTZ black hole

• URL: http://arxiv.org/abs/2108.10638v1
• Date: Tue, 24 Aug 2021 10:46:07 GMT
• Title: Cluster algebraic description of entanglement patterns for the BTZ black hole
• Authors: Bercel Boldis and P\'eter L\'evay
• Abstract summary: 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. We show that there is an underlying $C_N-1$ cluster algebra encoding entanglement patterns of the thermal state.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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