2 research outputs found
Toric Calabi-Yau supermanifolds and mirror symmetry
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.Comment: 20 pages, v2: references adde
On Local Calabi-Yau Supermanifolds and Their Mirrors
We use local mirror symmetry to study a class of local Calabi-Yau
super-manifolds with bosonic sub-variety V_b having a vanishing first Chern
class. Solving the usual super- CY condition, requiring the equality of the
total U(1) gauge charges of bosons \Phi_{b} and the ghost like fields \Psi_{f}
one \sum_{b}q_{b}=\sum_{f}Q_{f}, as \sum_{b}q_{b}=0 and \sum_{f}Q_{f}=0,
several examples are studied and explicit results are given for local A_{r}
super-geometries. A comment on purely fermionic super-CY manifolds
corresponding to the special case where q_{b}=0, \forall b and \sum_{f}Q_{f}=0
is also made.\bigskipComment: 17 page