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Opening Mirror Symmetry on the Quintic

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Abstract

Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. We hypothesize that 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 further check the conjecture by reproducing the first few instanton numbers by a localization computation directly in the A-model, and verifying Ooguri-Vafa integrality. This is the first exact result on open string mirror symmetry for a compact Calabi-Yau manifold.

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Authors and Affiliations

  1. School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, USA

    Johannes Walcher

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  1. Johannes Walcher
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Correspondence to Johannes Walcher.

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Communicated by N. A. Nekrasov

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Walcher, J. Opening Mirror Symmetry on the Quintic. Commun. Math. Phys. 276, 671–689 (2007). https://doi.org/10.1007/s00220-007-0354-8

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  • DOI: https://doi.org/10.1007/s00220-007-0354-8

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