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Cluster algebraic description of entanglement patterns for the BTZ black hole
- Publication Year :
- 2021
-
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.<br />Comment: 15 pages, 9 figures, LaTex
- Subjects :
- High Energy Physics - Theory
Mathematical Physics
Quantum Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2108.10638
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevD.105.046020