Super Calabi-Yau's and Special Lagrangians

Abstract

We apply mirror symmetry to the super Calabi-Yau manifold CP^{(n|n+1)} and show that the mirror can be recast in a form which depends only on the superdimension and which is reminiscent of a generalized conifold. We discuss its geometrical properties in comparison to the familiar conifold geometry. In the second part of the paper examples of special-Lagrangian submanifolds are constructed for a class of super Calabi-Yau's. We finally comment on their infinitesimal deformations.

20 pages, no figures, latex; v2: references added; v3: minor clarifications added, version published in JHEP

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• On gauge/string correspondence and mirror symmetry
• N=2 Superconformal Symmetry in Super Coset Models
• Topological String on Toric CY3s in Large Complex Structure Limit
• Twistor Strings with Flavour
• Monopoles, Dirac operator and index theory for fuzzy $SU(3)/(U(1)\times U(1))$
• Super Landau-Ginzburg mirrors and algebraic cycles