# 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…

## 34 Citations

On local Calabi?Yau supermanifolds and their mirrors

- Physics, Mathematics
- 2006

We use local mirror symmetry to study a class of local Calabi?Yau supermanifolds with bosonic sub-variety Vb having a vanishing first Chern class. Solving the usual super-CY condition, requiring the…

Super Calabi-Yau ’ s and Special Lagrangians

- Mathematics
- 2005

We apply mirror symmetry to the super Calabi-Yau manifold CP and show that the mirror can be recast in a form which depends only on the superdimension and which is reminiscent of a generalized…

Super Calabi-Yau's and special Lagrangians

- Mathematics
- 2007

We apply mirror symmetry to the super Calabi-Yau manifold CP(n|n+1) and show that the mirror can be recast in a form which depends only on the superdimension and which is reminiscent of a generalized…

Super Calabi-Yau ’ s and Special

- Mathematics
- 2005

We apply mirror symmetry to the super Calabi-Yau manifold CP (n|n+1) and show that the mirror can be recast in a form which depends only on the superdimension and which is reminiscent of a…

On hidden symmetries of a super gauge theory and twistor string theory

- Mathematics
- 2005

We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the -extented self-dual super Yang-Mills equations for general ≤ 4 by using…

Gauged linear sigma model on supermanifold

- Physics
- 2005

We formulate a gauged linear sigma model on a supermanifold. The structure of classical vacua is investigated and one-loop corrections are calculated for an auxiliary D-field. We find out a…

Quiver Gauge theories from Lie Superalgebras

- Mathematics
- 2012

We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex…

Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory

- Mathematics
- 2006

In this thesis, we report on results in non-anticommutative field theory and twistor string theory, trying to be self-contained. We first review the construction of non-anticommutative N=4 super…

String Theories on Flat Supermanifolds

- Physics, Mathematics
- 2005

We construct bosonic string theories, RNS string theories and heterotic string theories on flat supermanifolds. For these string theories, we show cancellations of the central charges and modular…

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