String theory on three dimensional black holes

TL;DR

This paper explores string theory on three-dimensional black holes using conformal field theory, analyzing the spectrum, ghost issues, and dualities, and discusses challenges in formulating consistent string models in curved spacetimes.

Contribution

It presents the first quantization attempt of string theory in a black hole background with infinite propagating modes, using an orbifold of the SL(2,R) WZW model.

Findings

Identified winding modes in the spectrum.

Demonstrated the presence of negative norm physical states.

Discovered a self-dual T-duality reversing black hole mass.

Abstract

We investigate the string theory on three dimensional black holes discovered by Ba\~{n}ados, Teitelboim and Zanelli in the framework of conformal field theory. The model is described by an orbifold of the $\widetilde{SL}(2,R)$ WZW model. The spectrum is analyzed by solving the level matching condition and we obtain winding modes. We then study the ghost problem and show explicit examples of physical states with negative norms. We discuss the tachyon propagation and the target space geometry, which are irrelevant to the details of the spectrum. We find a self-dual T-duality transformation reversing the black hole mass. We also discuss difficulties in string theory on curved spacetime and possibilities to obtain a sensible string theory on three dimensional black holes. This work is the first attempt to quantize a string theory in a black hole background with an infinite number of propagating modes.