Opening Mirror Symmetry on the Quintic

TL;DR

This paper uses mirror symmetry to compute open Gromov-Witten invariants for the quintic threefold, providing the first exact results on open string mirror symmetry in a compact Calabi-Yau.

Contribution

It introduces a method to determine open Gromov-Witten invariants via mirror symmetry, extending the Picard-Fuchs equation and verifying consistency across the moduli space.

Findings

Calculated the number of holomorphic disks ending on the real Lagrangian.

Verified monodromy consistency of the superpotential.

Reproduced instanton numbers and confirmed Ooguri-Vafa integrality.

Abstract

Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open Gromov-Witten invariants, satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space. We reproduce the first few instanton numbers by a localization computation directly in the A-model, and check Ooguri-Vafa integrality. This is the first exact result on open string mirror symmetry for a compact Calabi-Yau manifold.