Mirror Symmetry of Calabi-Yau Supermanifolds

TL;DR

This paper explores mirror symmetry in Calabi-Yau supermanifolds, specifically super Landau-Ginzburg models of WCP^{3|2}, revealing new elliptic and hypersurface fibrations with distinct dependencies on variables.

Contribution

It introduces novel mirror constructions for Calabi-Yau supermanifolds, expanding the understanding of their geometric and physical properties.

Findings

Identified elliptic fibration over complex plane with specific variable dependencies.

Described a Calabi-Yau hypersurface patch with different variable dependence.

Compared the behaviors of two mirror models in the context of super Landau-Ginzburg theories.

Abstract

We study super Landau-Ginzburg mirrors of the weighted projective superspace WCP^{3|2} which is a Calabi-Yau supermanifold and appeared in hep-th/0312171(Witten) in the topological B-model. One of them is an elliptic fibration over the complex plane whose coordinate is given in terms of two bosonic and two fermionic variables as well as Kahler parameter of WCP^{3|2}. The other is some patch of a degree 3 Calabi-Yau hypersurface in CP^2 fibered by the complex plane whose coordinate depends on both above four variables and Kahler parameter but its dependence behaves quite differently.