Correlation functions of gauged linear $\sigma$-model

TL;DR

This paper develops a mathematical framework for the gauged linear sigma model by defining correlation functions on specific geometric objects, assuming the existence of certain virtual moduli cycles.

Contribution

It introduces a rigorous definition of GLSM correlation functions on smooth rigidified r-spin curves, advancing the mathematical understanding of GLSM.

Findings

Defines GLSM correlation functions under certain assumptions.

Lays groundwork for further rigorous mathematical analysis of GLSM.

Connects GLSM to virtual moduli cycle theory.

Abstract

This is the second paper in a series following arXiv:1405.6352, on the construction of a mathematical theory of the gauged linear $\sigma$-model (GLSM). In this paper, assuming the existence of virtual moduli cycles and their certain properties, we define the correlation function of GLSM for a fixed smooth rigidified $r$-spin curve.