Toric Calabi–Yau supermanifolds and mirror symmetry

@article{Belhaj2005ToricCS,
  title={Toric Calabi–Yau supermanifolds and mirror symmetry},
  author={Adil Belhaj and Lalla Btissam Drissi and J{\o}rgen Rasmussen and E. H. Saidi and Abdellah Sebbar},
  journal={Journal of Physics A},
  year={2005},
  volume={38},
  pages={6405-6418}
}
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… 
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References

SHOWING 1-10 OF 24 REFERENCES
Mirror symmetry of Calabi-Yau supermanifolds
  • C. Ahn
  • Mathematics, Physics
  • 2005
We study super Landau–Ginzburg mirrors of the weighted projective superspace WCP3|2 which is a Calabi–Yau supermanifold and appeared in hep-th/0312171 in the topological B-model. One of them is an
Strings in Twistor Superspace and Mirror Symmetry
Supermanifolds, rigid manifolds and mirror symmetry
Mirror Symmetry and Supermanifolds
We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super-Landau-Ginzburg theories. In some cases the dual can be equivalent to a geometry. We apply this to some examples.
On Supertwistors, the Penrose-Ward Transform and N=4 super Yang-Mills Theory
It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP 3|4 as a target space is equivalent to holomorphic Chern-Simons (hCS) theory on the same
N=2 strings and the twistorial Calabi-Yau
We interpret the A and B model topological strings on CP^{3|4} as equivalent to open N=2 string theory on spacetime with signature (2,2), when covariantized with respect to SO(2,2) and
Heterotic string/F-theory duality from mirror symmetry
We use local mirror symmetry in type IIA string compactifications on Calabi–Yau n + 1 folds Xn+1 to construct vector bundles on (possibly singular) elliptically fibered Calabi–Yau n-folds Zn. The
On Ricci flat supermanifolds
We study the Ricci flatness condition on generic supermanifolds. It has been found recently that when the fermionic complex dimension of the supermanifold is one the vanishing of the super-Ricci
On Calabi-Yau supermanifolds II
We study when Calabi-Yau supermanifolds M(1|2) with one complex bosonic coordinate and two complex fermionic coordinates are super Ricci-flat, and find that if the bosonic manifold is compact, it
On Calabi-Yau supermanifolds
We study when Calabi-Yau supermanifolds M 1|2 with one complex bosonic coordinate and two complex fermionic coordinates are super Ricci-flat, and find that if the bosonic manifold is compact, it must
...
...