Sphere partition function of Calabi-Yau GLSMs

TL;DR

This paper presents a universal formula for the sphere partition function of Calabi-Yau GLSMs in hybrid phases, linking it to Givental's functions, Gamma class, and hybrid model data, with tests on abelian cases.

Contribution

It introduces a universal expression for the sphere partition function in hybrid phases of Calabi-Yau GLSMs, extending previous results to more general fibrations.

Findings

The formula applies to Landau-Ginzburg fibrations over base manifolds.

Connections to mirror symmetry and FJRW theory are established.

Tests on abelian GLSMs confirm the proposal's validity.

Abstract

The sphere partition function of Calabi-Yau gauged linear sigma models (GLSMs) has been shown to compute the exact Kaehler potential of the Kaehler moduli space of a Calabi-Yau. We propose a universal expression for the sphere partition function evaluated in hybrid phases of Calabi-Yau GLSMs that are fibrations of Landau-Ginzburg orbifolds over some base manifold. Special cases include Calabi-Yau complete intersections in toric ambient spaces and Landau-Ginzburg orbifolds. The key ingredients that enter the expression are Givental's I/J-functions, the Gamma class and further data associated to the hybrid model. We test the proposal for one- and two-parameter abelian GLSMs, making connections, where possible, to known results from mirror symmetry and FJRW theory.