AdS3 Orbifolds, BTZ Black Holes, and Holography

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.