c=1 String Theory as a Topological G/G Model

TL;DR

This paper demonstrates a correspondence between the $c=1$ string theory and a topological G/G model, revealing an equivalence in their Fock space cohomologies through BRST cohomology analysis.

Contribution

It establishes a novel equivalence between the $c=1$ string model and the $SL(2,R)/U(1)$ topological model at the cohomological level.

Findings

One-to-one correspondence between $k=-1$ model states and $c=1$ string states.

Full cohomological equivalence between $SL(2,R)/SL(2,R)$ and $SL(2,R)/U(1)$ models.

Abstract

The physical states on the free field Fock space of the ${SL(2,R)\over SL(2,R)$ model at any level are computed. Using a similarity transformation on $Q_{BRST}$, the cohomology of the latter is mapped into a direct sum of simpler cohomologies. We show a one to one correspondence between the states of the $k=-1$ model and those of the $c=1$ string model. A full equivalence between the ${SL(2,R)\over SL(2,R)$ and ${SL(2,R)\over U(1)$ models at the level of their Fock space cohomologies is found.