Entropy of Three-Dimensional Black Holes in String Theory

TL;DR

The paper shows that a three-dimensional BTZ black hole can be realized as a supersymmetric, RR-free compactification of heterotic string theory on AdS3 x S7, with a nontrivial dilaton and NS-NS flux. The extremal entropy computed from gravity matches a microscopic computation via the AdS3/CFT2 framework and Cardy formula, relying on a central charge c = 12 l. This provides a concrete realization of Susskind's idea to derive black hole entropy directly from fundamental string states. The work connects AdS3 geometry, supersymmetric compactifications, and CFT entropy counting, offering pathways to extend the approach to higher-dimensional AdS black holes.

Abstract

It is observed that the three-dimensional BTZ black hole is a supersymmetric solution of the low-energy field equations of heterotic string theory compactified on an Einstein space. The solution involves a non-zero dilaton and NS-NS H-field. The entropy of the extreme black hole can then be computed using string theory and the asymptotic properties of anti-de Sitter space, without recourse to a D-brane analysis. This provides an explicit example of a black hole whose entropy can be computed using fundamental string theory, as advocated by Susskind.