Open/closed Correspondence and Extended LG/CY Correspondence for Quintic Threefolds

TL;DR

This paper establishes a new open/closed correspondence for the quintic threefold by representing Walcher's disk potential as a central charge in an extended GLSM, linking open and closed invariants.

Contribution

It introduces the extended quintic GLSM and demonstrates its role in unifying open Landau-Ginzburg/Calabi-Yau correspondence and mirror symmetry with wall-crossing phenomena.

Findings

Disk potential as a central charge in extended GLSM

Open/closed correspondence for the quintic threefold

Compatibility of open mirror symmetry with wall-crossing

Abstract

We show that Walcher's disk potential for the quintic threefold can be represented as a central charge of a specific Gauged Linear Sigma Model which we call the extended quintic GLSM. This representation provides an open/closed correspondence for the quintic threefold since the central charge is a generating function of closed genus-zero GLSM invariants. We also explain how open Landau-Ginzburg/Calabi-Yau correspondence and open mirror symmetry for the quintic are compatible with wall-crossing and mirror symmetry of the extended GLSM, respectively.