Topological Field Theory Interpretations and LG Representation of c=1 String Theory

TL;DR

This paper explores the topological aspects of c=1 string theory at the self-dual radius, revealing two distinct topological structures and providing a Landau-Ginzburg representation for one, enhancing understanding of its mathematical framework.

Contribution

It identifies two different topological field theory structures in c=1 string theory and develops a Landau-Ginzburg model for one of these structures, extending the theoretical understanding.

Findings

Two topological field theory structures identified

Landau-Ginzburg representation constructed for one structure

Topological features persist under tachyonic perturbations

Abstract

We analyze the topological nature of $c=1$ string theory at the self--dual radius. We find that it admits two distinct topological field theory structures characterized by two different puncture operators. We show it first in the unperturbed theory in which the only parameter is the cosmological constant, then in the presence of any infinitesimal tachyonic perturbation. We also discuss in detail a Landau--Ginzburg representation of one of the two topological field theory structures.