Disc Instantons in Linear Sigma Models

Abstract

We construct a linear sigma model for open-strings ending on special Lagrangian cycles of a Calabi-Yau manifold. We illustrate the construction for the cases considered by Aganagic and Vafa in hep-th/0012041. This leads naturally to concrete models for the moduli space of open-string instantons. These instanton moduli spaces can be seen to be intimately related to certain auxiliary boundary toric varieties. By considering the relevant Gelfand-Kapranov-Zelevinsky (GKZ) differential equations of the boundary toric variety, we obtain the contributions to the worldvolume superpotential on the A-branes from open-string instantons. By using an ansatz due to Aganagic, Klemm and Vafa in hep-th/0105045, we obtain the relevant change of variables from the linear sigma model to the non-linear sigma model variables - the open-string mirror map. Using this mirror map, we obtain results in agreement with those of AV and AKV for the counting of holomorphic disc instantons.

1+32 pages, 1 figure, LaTeX2e; (v2) Tables and References added, typos fixed

References in corpus (5)

• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Disk Instantons, Mirror Symmetry and the Duality Web
• Framed knots at large N
• Linear Models of Supersymmetric D-Branes
• Instanton amplitudes in open-closed topological string theory

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• D-branes and Normal Functions
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• Summing up Open String Instantons and N=1 String Amplitudes
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• Moduli Webs and Superpotentials for Five-Branes
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• Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry
• A Geometrical Construction of Rational Boundary States in Linear Sigma Models
• On A-twisted moduli stack for curves from Witten's gauged linear sigma models
• Symplectic cuts and open/closed strings II
• Symplectic cuts and open/closed strings I