The Spectrum of Sl(2, R)/U(1) Black Hole Conformal Field Theory

TL;DR

This paper analyzes the $SL(2, R)/U(1)$ black hole conformal field theory, determining its spectrum and vertex operators, and explores the use of supersymmetric quantum mechanics in non-linear sigma models.

Contribution

It provides an explicit spectrum and vertex operators for the $SL(2, R)/U(1)$ CFT and discusses supersymmetric quantum mechanics applications to non-linear sigma models.

Findings

Spectrum explicitly determined using supersymmetric quantum mechanics

Vertex operators expressed in terms of Jacobi functions

Discussion on SUSY QM techniques for non-linear sigma models

Abstract

We study string theory in the background of a two-dimensional black hole which is described by an $SL(2, R)/U(1)$ coset conformal field theory. We determine the spectrum of this conformal field theory using supersymmetric quantum mechanics and give an explicit form of the vertex operators in terms of the Jacobi functions. We also discuss the applicability of SUSY quantum mechanics techniques to non-linear $\sigma$-models.