Winding strings and AdS_3 black holes

TL;DR

This paper systematically studies string theory in AdS_3 black hole backgrounds, analyzing geodesics, spectra, classical winding strings, and boundary Virasoro algebra, clarifying aspects of the AdS3/CFT correspondence.

Contribution

It provides a detailed analysis of string dynamics in BTZ black holes, including geodesics, spectra, classical winding solutions, and boundary algebra formulation, advancing understanding of AdS_3/CFT.

Findings

Analysis of geodesic structure in BTZ black holes

Construction of classical winding strings around black holes

Linking ghost-free spectrum proposals to the massless black hole background

Abstract

We start a systematic study of string theory in AdS_3 black hole backgrounds. Firstly, we analyse in detail the geodesic structure of the BTZ black hole, including spacelike geodesics. Secondly, we study the spectrum for massive and massless scalar fields, paying particular attention to the connection between Sl(2,R) subgroups, the theory of special functions and global properties of the BTZ black holes. We construct classical strings that wind the black holes. Finally, we apply the general formalism to the vacuum black hole background, and formulate the boundary spacetime Virasoro algebra in terms of worldsheet operators. We moreover establish the link between a proposal for a ghost free spectrum for Sl(2,R) string propagation and the massless black hole background, thereby claryfing aspects of the AdS3/CFT correspondence.