AdS 3 orbifolds, BTZ black holes, and holography

Abstract

Abstract Conical defects of the form (AdS 3 × S 3 $$ {\mathbbm{S}}^3 $$ )/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. the hyperbolic ball ℍ 3 + $$ {\mathbb{H}}_3^{+} $$ ) and consider the orbifold by any infinite discrete (Kleinian) group generated by a set of elliptic elements γ i ∈ SL(2, ℂ), γ i k i $$ {\gamma}_i^{{\textrm{k}}_i} $$ = 𝟙, i = 1, . . . , K. The resulting geometry consists of multiple conical defects traveling along geodesics in ℍ 3 + $$ {\mathbb{H}}_3^{+} $$ , and provides a semiclassical bulk description of correlation functions in the dual CFT involving the corresponding defect operators, which is nonperturbatively exact in α ′. 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.

Keywords

• AdS-CFT Correspondence
• Black Holes in String Theory
• Conformal Field Models in String Theory