Towards a mirror theorem for GLSMs

TL;DR

This paper introduces a new method for computing genus-zero invariants of gauged linear sigma models (GLSMs), connecting quasimap invariants and I-functions, with explicit formulas for torus groups and validation against known cases.

Contribution

It presents a novel approach to compute GLSM invariants using derivatives of I-functions, including a new construction applicable under proper evaluation maps and light insertions.

Findings

Derived explicit I-function formulas for GLSMs with torus groups

Validated the approach by matching with known special cases

Established a new construction for GLSM invariants with proper evaluation maps

Abstract

We propose a method for computing generating functions of genus-zero invariants of a gauged linear sigma model $(V, G, \theta, w)$. We show that certain derivatives of $I$-functions of quasimap invariants of $[V //_\theta G]$ produce $I$-functions (appropriately defined) of the GLSM. When $G$ is an algebraic torus we obtain an explicit formula for an $I$-function, and check that it agrees with previously computed $I$-functions in known special cases. Our approach is based on a new construction of GLSM invariants which applies whenever the evaluation maps from the moduli space are proper, and includes insertions from light marked points.