Super Picard-Fuchs Equation and Monodromies for Supermanifolds

TL;DR

This paper investigates the Picard-Fuchs equations and monodromies of super Calabi-Yau mirror manifolds, deriving explicit solutions and mirror hypersurfaces in super Landau-Ginzburg models.

Contribution

It provides a detailed analysis of Picard-Fuchs equations, monodromies, and mirror hypersurfaces for super Calabi-Yau manifolds using advanced mathematical techniques.

Findings

Derived Meijer basis solutions for super Landau-Ginzburg mirrors

Computed monodromies at key points in moduli space

Constructed explicit mirror hypersurfaces in super projective spaces

Abstract

Following [1] and [2], we discuss the Picard-Fuchs equation for the super Landau-Ginsburg mirror to the super-Calabi-Yau in WCP^(3|2)[1,1,1,3|1,5], (using techniques of [3,4]) Meijer basis of solutions and monodromies (at 0,1 and \infty) in the large and small complex structure limits, as well as obtain the mirror hypersurface, which in the large Kaehler limit, turns out to be either a bidegree-(6,6) hypersurface in WCP^(3|1)[1,1,1,2] x WCP^(1|1)[1,1|6] or a (Z_2-singular) bidegree-(6,12) hypersurface in WCP^(3|1)[1,1,2,6|6] x WCP^(1|1)[1,1|6].