Bosonization of a Topological Coset Model and Non-Critical String Theory

TL;DR

This paper explores the connection between a topological coset model based on super $SL(2,R)/U(1)$ and non-critical string theory, revealing how their algebraic structures and operators relate through free field realization.

Contribution

It demonstrates the transformation of the twisted N=2 algebra of the coset model into that of non-critical string theory and identifies screening operators with key elements of string dynamics.

Findings

Twisted N=2 algebra maps to non-critical string algebra.

Screening operators correspond to minimal matter or cosmological constant.

An intrinsic screening operator becomes a BRST nontrivial state in ghost number zero.

Abstract

We analyze the relation between a topological coset model based on super $SL(2,R)/U(1)$ coset and non-critical string theory by using free field realization. We show that the twisted $N=2$ algebra of the coset model can be naturally transformed into that of non-critical string. The screening operators of the coset models can be identified either with those of the minimal matters or with the cosmological constant operator. We also find that another screening operator, which is intrinsic in our approach, becomes the BRST nontrivial state of ghost number $0$ (generator of the ground ring for $c=1$ gravity).