The spectrum of strings on BTZ black holes and spectral flow in the SL(2,R) WZW model

TL;DR

This paper investigates the spectrum of bosonic strings on rotating BTZ black holes using an SL(2,R) WZW model, highlighting the role of spectral flow in generating twisted sectors and understanding quantum number quantization.

Contribution

It demonstrates how spectral flow in the WZW model can generate twisted sectors for strings on BTZ black holes, providing insights into the spectrum and quantization conditions.

Findings

Spectral flow generates twisted sectors in the string spectrum.

Quantization conditions relate to anomalies in conserved currents.

Connection between spectral flow and orbifold techniques established.

Abstract

We study the spectrum of bosonic string theory on rotating BTZ black holes, using a SL(2,R) WZW model. Previously, Natsuume and Satoh have analyzed strings on BTZ black holes using orbifold techniques. We show how an appropriate spectral flow in the WZW model can be used to generate the twisted sectors, emphasizing how the spectral flow works in the hyperbolic basis natural for the BTZ black hole. We discuss the projection condition which leads to the quantization condition for the allowed quantum numbers for the string excitations, and its connection to the anomaly in the corresponding conserved Noether current.