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arXiv · hep-th/9806195

AdS_3 Gravity and Conformal Field Theories

Klaus Behrndt·Ilka Brunner·Ingo Gaida
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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 $AdS_3 \times S^3$ 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 $α^\prime$, 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.

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Klaus Behrndt, Ilka Brunner, Ingo Gaida. 1998-07-28. AdS_3 Gravity and Conformal Field Theories. https://doi.org/10.1016/s0550-3213(99)00040-1

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