BTZ black hole entropy from a Chern–Simons matrix model

DOI10.1088/0264-9381/30/23/235016zbMATH Open1284.83069arXiv1306.0169OpenAlexW3104202777MaRDI QIDQ5746894

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Publication date: 10 February 2014

Published in: (Search for Journal in Brave)

Abstract: We examine a Chern-Simons matrix model which we propose as a toy model for studying the quantum nature of black holes in 2+1 gravity. Its dynamics is described by two $NimesN$ matrices, representing the two spatial coordinates. The model possesses an internal SU(N) gauge symmetry, as well as an external rotation symmetry. The latter corresponds to the rotational isometry of the BTZ solution, and does not decouple from SU(N) gauge transformations. The system contains an invariant which is quadratic in the spatial coordinates. We obtain its spectrum and degeneracy, and find that the degeneracy grows exponentially in the large $N$ limit. The usual BTZ black hole entropy formula is recovered upon identifying the quadratic invariant with the square of the black hole horizon radius. The quantum system behaves collectively as an integer (half-integer) spin particle for even (odd) $N$ under $2pi$-rotations.

Full work available at URL: https://arxiv.org/abs/1306.0169

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