On genus-0 invariants of Calabi-Yau hybrid models

TL;DR

This paper computes genus zero correlators of Calabi-Yau hybrid models, generalizing Gromov-Witten and FJRW invariants, and verifies their consistency with mirror symmetry and FJRW theory.

Contribution

It introduces a method to compute genus zero invariants of Calabi-Yau hybrid models using GLSM partition functions and extracts the associated I- and J-functions.

Findings

Computed invariants for specific hybrid models

Matched results with mirror symmetry predictions

Extended the understanding of Landau-Ginzburg orbifold phases

Abstract

We compute genus zero correlators of hybrid phases of Calabi-Yau gauged linear sigma models (GLSMs), i.e. of phases that are Landau-Ginzburg orbifolds fibered over some base. These correlators are generalisations of Gromov-Witten and FJRW invariants. Using previous results on the structure of the of the sphere- and hemisphere partition functions of GLSMs when evaluated in different phases, we extract the I-function and the J-function from a GLSM calculation. The J-function is the generating function of the correlators. We use the field theoretic description of hybrid models to identify the states that are inserted in these correlators. We compute the invariants for examples of one- and two-parameter hybrid models. Our results match with results from mirror symmetry and FJRW theory.