Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole

TL;DR

This paper computes the one-loop partition function for Euclidean BTZ black holes in AdS_3, revealing the spectrum includes long strings and discrete states, consistent with previous findings, and emphasizing modular invariance.

Contribution

It provides a detailed calculation of the one-loop partition function for Euclidean BTZ black holes, confirming spectral features and modular invariance in the SL(2,R) WZW model.

Findings

Spectrum includes long strings and discrete states.

Partition function is modular invariant.

Results align with previous spectral analyses.

Abstract

We consider the one-loop partition function for Euclidean BTZ black hole backgrounds or equivalently thermal AdS_3 backgrounds which are quotients of H_3 (Euclidean AdS_3). The one-loop partition function is modular invariant and we can read off the spectrum which is consistent to that found in hep-th/0001053. We see long strings and discrete states in agreement with the expectations.