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arXiv · hep-th/0410291

Toric Calabi-Yau supermanifolds and mirror symmetry

A. Belhaj·L. B. Drissi·J. Rasmussen·E. H. Saidi·A. Sebbar
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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.

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A. Belhaj, L. B. Drissi, J. Rasmussen, E. H. Saidi, A. Sebbar. 2004-11-14. Toric Calabi-Yau supermanifolds and mirror symmetry. https://doi.org/10.1088/0305-4470%2F38%2F28%2F013

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