Topological Structure in ${\hat c}=1$ Fermionic String Theory

TL;DR

This paper reveals that the $ ilde{c}=1$ fermionic string theory decomposes into a topological part and an irrelevant part, with the topological structure explaining the physical spectrum and relating to a hidden $N=2$ superconformal algebra.

Contribution

It demonstrates the decomposition of $ ilde{c}=1$ fermionic string theory into a topological component and uncovers a hidden $N=2$ superconformal algebra within the $N=3$ algebra.

Findings

The theory decomposes into independent parts, one topological.

The physical spectrum is explained by the topological structure.

A hidden $N=2$ superconformal algebra is identified.

Abstract

$\chat=1$ fermionic string theory, which is considered as a fermionic string theory in two dimension, is shown to decompose into two mutually independent parts, one of which can be viewed as a topological model and the other is irrelevant for the theory. The physical contents of the theory is largely governed by this topological structure, and the discrete physical spectrum of $\chat=1$ string theory is naturally explained as the physical spectrum of the topological model. This topological structure turns out to be related with a novel hidden $N=2$ superconformal algebra (SCA) in the enveloping algebra of the $N=3$ SCA in fermionic string theories.