AdS 3 gravity and conformal field theories

Abstract

We present a detailed analysis of AdS 3 gravity, the BTZ black hole and the associated conformal field theories (CFTs). In particular we focus on the non-extreme six-dimensional string solution with background metric AdS 3 × S 3 near the horizon. In addition we introduce momentum modes along the string, corresponding to a BTZ black hole, and a Taub-NUT soliton in the transverse Euclidean space. We show that the AdS 3 space-time of this configuration has the spatial geometry of an annulus with a Liouville model at the outer boundary and a two-dimensional black hole at the inner boundary. These CFTs provide the dynamical degrees of freedom of the three-dimensional effective model and, together with the CFT corresponding to S 3, provide a statistical interpretation of the corresponding Bekenstein-Hawking entropy. We test the proposed exact black hole entropy, which should hold to all orders in α′, by an independent field theoretical analysis including higher-order curvature corrections. We find consistent results that yield a renormalization of the classical parameters, only. In addition we find a logarithmic subleading black hole entropy coming from gravitational fivebrane instantons in a special limit in moduli space.