A. Chaney, Lei Lu, A. Stern
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 $N\times N$ 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 a unique 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 unique quadratic invariant with the square of the black hole horizon radius.
View original:
http://arxiv.org/abs/1306.0169
No comments:
Post a Comment