BRST Analysis of Physical States in Two-Dimensional Black Hole

TL;DR

This paper analyzes the BRST cohomology of a two-dimensional string black hole model, revealing a rich spectrum of physical states including discrete and new states with various ghost numbers.

Contribution

It provides a detailed BRST analysis of the $SL(2,R)/U(1)$ coset model, uncovering new physical states beyond known discrete states in 2D gravity.

Findings

Identification of additional physical states with ghost number -1 to 2

Presence of discrete states similar to $c=1$ 2D gravity

Discussion of characters for nonunitary representations

Abstract

We study the BRST cohomology for $SL(2,R)/U(1)$ coset model, which describes an exact string black hole solution. It is shown that the physical spectrum could contain not only the extra discrete states corresponding to those in $c=1$ two-dimensional gravity but also many additional new states with ghost number $N_{FP}= -1 \sim 2$. We also discuss characters for nonunitary representations and the relation of our results to other approaches.