Topological 2D String Theory: Higher-genus Amplitudes and W-infinity Identities

TL;DR

This paper explores topological 2D string theory with a specific superpotential, analyzing higher-genus amplitudes and their relation to W-infinity algebra, using intersection theory and Landau-Ginzburg models.

Contribution

It provides a detailed solution for higher-genus amplitudes in topological string theory with a singular superpotential, revealing their algebraic structure.

Findings

Higher-genus amplitudes decompose into bulk and boundary contributions

Generated amplitudes form the W-infinity algebra

The theory is a topological version of the c=1 string at the self-dual radius

Abstract

We investigate Landau-Ginzburg string theory with the singular superpotential X^{-1} on arbitrary Riemann surfaces. This theory, which is a topological version of the c=1 string at the self-dual radius, is solved using results from intersection theory and from the analysis of matter Landau-Ginzburg systems, and consistency requirements. Higher-genus amplitudes decompose as a sum of contributions from the bulk and the boundary of moduli space. These amplitudes generate the W-infinity algebra.