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

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.