Open string instantons and relative stable morphisms

Abstract

We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri and Vafa from the point of view of physics. By using the method of virtual localization, we successfully reproduce their results for multiple covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold of a Calabi-Yau 3-fold, by Riemann surfaces with arbitrary genera and number of boundary components. In particular we show that in the case we consider there are no open string instantons with more than one boundary component ending on the Lagrangian submanifold.

This is the version published by Geometry & Topology Monographs on 22 April 2006

References in corpus (3)

• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
• A degeneration of stable morphisms and relative stable morphisms

Cited by in corpus (7)

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• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants
• Superpotentials of D-branes in Calabi-Yau Manifolds with Several Moduli by Mirror Symmetry and Blown-up