Super Calabi-Yau's and Special Lagrangians
Riccardo Ricci
TL;DR
This paper explores mirror symmetry for super Calabi-Yau manifolds, revealing a simplified mirror structure dependent on superdimension, and constructs special Lagrangian submanifolds with their deformations.
Contribution
It introduces a new form of mirror symmetry for super Calabi-Yau manifolds and constructs examples of special Lagrangian submanifolds within this framework.
Findings
Mirror of super Calabi-Yau depends only on superdimension
Mirror resembles a generalized conifold
Constructed examples of special Lagrangian submanifolds
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.
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