AdS_3 Gravity and Conformal Field Theories

TL;DR

This paper analyzes $AdS_3$ gravity, BTZ black holes, and related conformal field theories, providing insights into their geometry, entropy, and quantum corrections, with implications for string theory and holography.

Contribution

It introduces a detailed analysis of $AdS_3$ backgrounds with string solutions, connecting them to CFTs and black hole entropy, including higher-order corrections and instanton effects.

Findings

$AdS_3$ space has an annulus geometry with boundary CFTs.

The black hole entropy matches field theory predictions including higher-order corrections.

Logarithmic entropy corrections arise from gravitational fivebrane instantons.

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 $\alpha^\prime$, 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.