AdS3 Orbifolds, BTZ Black Holes, and Holography

TL;DR

This paper explores the construction of AdS3 orbifolds with conical defects, their relation to BTZ black holes, and their role in holography, providing exact string theory descriptions and insights into black hole microstates.

Contribution

It derives exact orbifold descriptions of AdS3 geometries with defects from gauged WZW models and connects these to black hole formation and microstates in holography.

Findings

Exact orbifold descriptions of conical defects in string theory.

Semiclassical bulk description of defect correlators in dual CFT.

Geometric interpretation of black hole formation from defect collisions.

Abstract

Conical defects of the form $(AdS_3\times S^3)/Z_k$ have an exact orbifold description in worldsheet string theory, which we derive from their known presentation as gauged Wess-Zumino-Witten models. The configuration of strings and fivebranes sourcing this geometry is well-understood, as is the correspondence to states/operators in the dual $CFT_2$. One can analytically continue the construction to Euclidean $AdS_3$ (i.e. $H_3^+$) and consider the orbifold by any infinite discrete (Kleinian) group generated by a set of elliptic (rotational) elements. The resulting geometry consists of multiple conical defects traveling along geodesics in $H_3^+$, and provides a semiclassical bulk description of correlation functions in the dual CFT involving the corresponding defect operators, which is nonperturbatively exact in $\alpha'$. The Lorentzian continuation of these geometries describes a collection of defects colliding to make a BTZ black hole. We comment on a recent proposal to use such correlators to prepare a basis of black hole microstates, and elaborate on a picture of black hole formation and evaporation in terms of the underlying brane dynamics in the bulk.