String theory on three dimensional black holes

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.

35 pages, LaTeX, norms of negative norm states are corrected and minor corrections

References in corpus (4)

• The (2+1)-Dimensional Black Hole
• Extreme dyonic black holes in string theory
• Exactly solvable string models of curved space-time backgrounds
• Ghost-Free Spectrum of a Quantum String in SL(2,R) Curved Spacetime

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