Massless BTZ black holes in minisuperspace

TL;DR

This paper investigates string propagation on massless BTZ black holes by analyzing the SL(2,R) WZW model in minisuperspace, deriving new group-theoretic results, and exploring implications for string theory in Lorentzian geometries.

Contribution

It provides a detailed analysis of the SL(2,R) WZW model for massless BTZ black holes, including new results on Clebsch-Gordan coefficients and insights into string dynamics in Lorentzian backgrounds.

Findings

Derived new Clebsch-Gordan coefficients for SL(2,R) in a parabolic basis.

Analyzed two- and three-point functions in the minisuperspace limit.

Commented on applications to string theory in Lorentzian orbifolds and AdS/CFT.

Abstract

We study aspects of the propagation of strings on BTZ black holes. After performing a careful analysis of the global spacetime structure of generic BTZ black holes, and its relation to the geometry of the SL(2,R) group manifold, we focus on the simplest case of the massless BTZ black hole. We study the SL(2,R) Wess-Zumino-Witten model in the worldsheet minisuperspace limit, taking into account special features associated to the Lorentzian signature of spacetime. We analyse the two- and three-point functions in the pointparticle limit. To lay bare the underlying group structure of the correlation functions, we derive new results on Clebsch-Gordan coefficients for SL(2,R) in a parabolic basis. We comment on the application of our results to string theory in singular time-dependent orbifolds, and to a Lorentzian version of the AdS/CFT correspondence.