Toric Calabi-Yau supermanifolds and mirror symmetry

Abstract

We study mirror symmetry of supermanifolds constructed as fermionic extensions of compact toric varieties. We mainly discuss the case where the linear sigma A-model contains as many fermionic fields as there are U(1) factors in the gauge group. In the mirror super-Landau-Ginzburg B-model, focus is on the bosonic structure obtained after integrating out all the fermions. Our key observation is that there is a relation between the super-Calabi-Yau conditions of the A-model and quasi-homogeneity of the B-model, and that the degree of the associated superpotential in the B-model is given in terms of the determinant of the fermion charge matrix of the A-model.

20 pages, v2: references added

Cited by in corpus (13)

• The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations
• Self-Dual Supergravity and Twistor Theory
• Fuzzy Toric Geometries
• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
• Graph Theory and Qubit Information Systems of Extremal Black Branes
• Super Calabi-Yau's and Special Lagrangians
• N=2 Superconformal Symmetry in Super Coset Models
• On Local Calabi-Yau Supermanifolds and Their Mirrors
• Toric Geometry and String Theory Descriptions of Qudit Systems
• Superconformal Symmetry in Linear Sigma Model on Supermanifolds
• Fano hypersurfaces and Calabi-Yau supermanifolds
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Einstein metrics on homogeneous superspaces