Towards a mirror theorem for GLSMs
Mark Shoemaker
TL;DR
This work advances a mirror-theoretic framework for gauged linear sigma models (GLSMs) by linking genus-zero GLSM invariants to derivatives of quasimap Gromov-Witten I-functions on the GIT quotient Y. The authors introduce compact-type GLSM invariants and show they arise naturally via 0+ stability and light marked points, enabling big I-functions that encode full genus-zero GLSM data. A central result expresses GLSM I-functions as derivatives of the Y-I-function, with an explicit toric formula in the abelian case, and aligns with known invariants in affine, geometric, and hybrid models. The paper provides a practical computational toolkit, unifies several strands of GLSM theory, and offers concrete comparisons to FJRW, complete intersections, and hybrid theories, enhancing the transfer of GW/mirror results to GLSMs.
Abstract
We propose a method for computing generating functions of genus-zero invariants of a gauged linear sigma model $(V, G, θ, w)$. We show that certain derivatives of $I$-functions of quasimap invariants of $[V //_θG]$ 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.