The partition function of the supersymmetric two-dimensional black hole and little string theory

TL;DR

This paper calculates the partition function of a supersymmetric 2D black hole model, decomposes it into superconformal characters, and explores its relation to little string theory and NS5-brane backgrounds.

Contribution

It provides a detailed computation of the partition function for the supersymmetric 2D black hole and establishes its connection to little string theory and NS5-brane configurations.

Findings

Identification of puzzling sectors of states in the partition function

Explicit correspondence between the black hole background and little string theory

Analysis of GSO projection effects on target space geometry

Abstract

We compute the partition function of the supersymmetric two-dimensional Euclidean black hole geometry described by the SL(2,R)/U(1) superconformal field theory. We decompose the result in terms of characters of the N=2 superconformal symmetry. We point out puzzling sectors of states besides finding expected discrete and continuous contributions to the partition function. By adding an N=2 minimal model factor of the correct central charge and projecting on integral N=2 charges we compute the partition function of the background dual to little string theory in a double scaling limit. We show the precise correspondence between this theory and the background for NS5-branes on a circle, due to an exact description of the background as a null gauging of SL(2,R) x SU(2). Finally, we discuss the interplay between GSO projection and target space geometry.