Towards a mirror theorem for GLSMs

Abstract

We propose a method for computing generating functions of genus-zero invariants of a gauged linear sigma model $(V,G,\hat{I}¸,w)$. We show that certain derivatives of $I$-functions of quasimap invariants of $[V/{/}_{\hat{I}}¸G]$ 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.

Final version, to appear in Compositio Mathematica