Determinantal Calabi-Yau varieties in Grassmannians and the Givental $I$-functions

TL;DR

This paper studies determinantal Calabi-Yau varieties in Grassmannians, providing explicit constructions and a method to compute their genus-0 Gromov-Witten invariants using Givental $I$-functions derived from supersymmetric localization.

Contribution

It introduces a new approach to explicitly construct determinantal Calabi-Yau varieties and compute their genus-0 Gromov-Witten invariants via Givental $I$-functions from gauged linear sigma models.

Findings

Explicit construction of determinantal Calabi-Yau varieties in Grassmannians.

An algorithm to evaluate genus-0 Gromov-Witten invariants using $I$-functions.

Results consistent with previous known examples.

Abstract

We examine a class of Calabi-Yau varieties of the determinantal type in Grassmannians and clarify what kind of examples can be constructed explicitly. We also demonstrate how to compute their genus-0 Gromov-Witten invariants from the analysis of the Givental $I$-functions. By constructing $I$-functions from the supersymmetric localization formula for the two dimensional gauged linear sigma models, we describe an algorithm to evaluate the genus-0 A-model correlation functions appropriately. We also check that our results for the Gromov-Witten invariants are consistent with previous results for known examples included in our construction.