Topological Landau-Ginzburg Model of Two-Dimensional String Theory

TL;DR

This paper explores a topological Landau-Ginzburg model with superpotential X^{-1}, establishing its equivalence to c=1 string theory at the self-dual radius, and computes correlation functions aligning with matrix-model predictions.

Contribution

It introduces a topological Landau-Ginzburg framework for c=1 string theory and computes key correlation functions, including genus one tachyon two-point functions.

Findings

Tree-level tachyon correlation functions match matrix-model results

Contact terms and operator flows are analyzed within the model

Genus one tachyon two-point function is obtained using modified recursion relations

Abstract

We study a topological Landau-Ginzburg model with superpotential W(X)=X^{-1}. This is argued to be equivalent to c=1 string theory compactified at the self-dual radius. We compute the tree-level correlation function of N tachyons in this theory and show their agreement with matrix-model results. We also discuss the nature of contact terms, the perturbed superpotential and the flow of operators in the small phase space. The role of gravitational descendants in this theory is examined, and the tachyon two-point function in genus 1 is obtained using a conjectured modification of the gravitational recursion relations.