What we don't know about BTZ black hole entropy

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Abstract
With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important to understand the `statistical mechanics' of the (2 + 1)-dimensional black hole of Bañados, Teitelboim, and Zanelli (BTZ). Several conformal field theoretic derivations of the BTZ entropy exist, but none is completely satisfactory, and many questions remain open: there is no consensus as to what fields provide the relevant degrees of freedom or where these excitations live. In this paper, I review some of the unresolved problems and suggest avenues for their solution.