The Partition Function of the Two-Dimensional Black Hole Conformal Field Theory

TL;DR

This paper calculates the partition function of the 2D black hole conformal field theory, confirming spectral properties and providing insights relevant to string theory backgrounds with SL(2,R)/U(1) factors.

Contribution

It provides the first path-integral computation of the partition function for the 2D black hole CFT, aligning with algebraic expectations and clarifying the spectrum.

Findings

Spectrum matches algebraic predictions

Confirmed bounds on discrete representation spin

Determined density of continuous representations

Abstract

We compute the partition function of the conformal field theory on the two-dimensional euclidean black hole background using path-integral techniques. We show that the resulting spectrum is consistent with the algebraic expectations for the SL(2,R)/U(1) coset conformal field theory construction. In particular, we find confirmation for the bound on the spin of the discrete representations and we determine the density of the continuous representations. We point out the relevance of the partition function to all string theory backgrounds that include an SL(2,R)/U(1) coset factor.