Disc Instantons in Linear Sigma Models

Details Disc Instantons in Linear Sigma Models Disc Instantons in Linear Sigma Models

2001-08-31

arxiv.org/abs/hep-th/0108234v2

Nucl.Phys.B646:498-523,2002

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/S0550-3213(02)00901-X

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.

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