String theory on three dimensional black holes

TL;DR

The paper analyzes string theory on the BTZ black hole by formulating an orbifold of the $\widetilde{SL}(2,\mathbf{R})$ WZW model and constructing its conformal field theory. It derives the spectrum including twisted sectors via level matching, then shows explicit negative-norm states that signal unitarity problems in the orbifold, despite a rich structure of Kac-Moody primaries. The work also investigates tachyon propagation, global geometry, and a self-dual T-duality that reverses the black hole mass, highlighting deep challenges in string theory on curved spacetimes. It concludes with a discussion of consistency conditions and possible spectrum-truncation or modified-current approaches required for a sensible theory in this background.

Abstract

We investigate the string theory on three dimensional black holes discovered by Bañados, 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.