Higgs-Coulomb correspondence and Wall-Crossing in abelian GLSMs

TL;DR

This paper develops a mathematical framework connecting Higgs and Coulomb phases in abelian GLSMs, providing explicit formulas for central charges and proving wall-crossing phenomena.

Contribution

It introduces the Higgs-Coulomb correspondence via integral formulas and uses it to establish GIT stability wall-crossing for central charges in abelian GLSMs.

Findings

Explicit integral formulas for central charges in Calabi-Yau cases

Proof of GIT stability wall-crossing using Higgs-Coulomb correspondence

Analytic continuation of central charges through integral representations

Abstract

We compute I-functions and central charges for abelian GLSMs using virtual matrix factorizations of Favero and Kim. In the Calabi-Yau case we provide analytic continuation for the central charges by explicit integral formulas. The integrals in question are called hemisphere partition functions and we call the integral representation Higgs-Coulomb correspondence. We then use it to prove GIT stability wall-crossing for central charges.