Mirror Symmetry and Supermanifolds

Abstract

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. In particular we show that the mirror of the twistorial Calabi-Yau CP^{3|4} becomes equivalent to a quadric in CP^{3|3} x CP^{3|3} as had been recently conjectured (in the limit where the Kähler parameter of CP^{3|4} t -> \pm \infty). Moreover, we show using these techniques that there is a non-trivial Z_2 symmetry for the Kähler parameter, t -> -t, which exchanges the opposite helicity states. As another class of examples, we show that the mirror of certain weighted projective (n+1|1) superspaces is equivalent to compact Calabi-Yau hypersurfaces in weighted projective n-space.

15 pages

References in corpus (4)

• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• Cubic Twistorial String Field Theory
• Supermanifolds, Rigid Manifolds and Mirror Symmetry
• Sigma-models having supermanifolds as target spaces

Cited by in corpus (43)

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• The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
• MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos
• Cubic Twistorial String Field Theory
• Ghost D-branes
• A Note on Twistor Gravity Amplitudes
• An ambitwistor Yang-Mills Lagrangian
• Conformal Sigma-Models on Supercoset Targets
• The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations
• Open BPS Wall Crossing and M-theory
• Topological B-Model on Weighted Projective Spaces and Self-Dual Models in Four Dimensions
• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• The Sigma Model on Complex Projective Superspaces
• Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory
• Super-Chern-Simons Theory as Superstring Theory
• A proposal for nonabelian (0,2) mirrors
• Conformal invariance and quantum integrability of sigma models on symmetric superspaces
• Six-Quark Amplitudes from Fermionic MHV Vertices
• Orbifolding the Twistor String
• Strings in Twistor Superspace and Mirror Symmetry
• Topological strings and their physical applications
• The Topological B-Model on Fattened Complex Manifolds and Subsectors of N=4 Self-Dual Yang-Mills Theory
• Self-Dual Supergravity and Twistor Theory
• Supertwistors and Cubic String Field Theory for Open N=2 Strings
• Projective Superspaces in Practice
• A Six Dimensional View on Twistors
• Graph Theory and Qubit Information Systems of Extremal Black Branes
• A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory
• Flux Vacua and Supermanifolds
• A proposal for (0,2) mirrors of toric varieties
• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• Toric Geometry and String Theory Descriptions of Qudit Systems
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• String Theories on Flat Supermanifolds
• Gauged Linear Sigma Model on Supermanifold
• Yang-Mills gravity in biconformal space
• Superconformal Symmetry in Linear Sigma Model on Supermanifolds
• Integration of Superforms and Super-Thom Class
• Non Projected Calabi-Yau Supermanifolds over ${\mathbb{P}}^2$
• On Calabi-Yau supermanifolds
• On perturbative field theory and twistor string theory