Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models

Abstract

Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N=(2,2) nonlinear sigma-models. The most direct relation is obtained at the N=(1,1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N=(2,2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kahler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.

arXiv comment20 pages, 2 figures, Journal Version

References in corpus (19)

• Poisson Structure Induced (Topological) Field Theories
• Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds
• Current Algebras and Differential Geometry
• Generalized complex manifolds and supersymmetry
• Generalized Calabi-Yau manifolds
• Topological sigma-models with H-flux and twisted generalized complex manifolds
• Generalized N=(2,2) Supersymmetric Non-Linear Sigma Models
• A sigma model field theoretic realization of Hitchin's generalized complex geometry
• N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models
• Poisson geometry of sigma models with extended supersymmetry
• Mirror symmetry for topological sigma models with generalized Kahler geometry
• Properties of Semi-Chiral Superfields
• D-branes in N=2 WZW models
• Generalized complex geometry and the Poisson Sigma Model
• The Geometry of Sigma-Models with Twisted Supersymmetry
• Geometry of D-branes for general N=(2,2) sigma models
• Generalized complex geometry and supersymmetric non-linear sigma models
• The Geometry of Supersymmetric Sigma-Models
• Geometry, Isometries and Gauging of (2,1) Heterotic Sigma-Models

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• Generalized Kahler manifolds and off-shell supersymmetry
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• A-branes and Noncommutative Geometry
• NS-NS fluxes in Hitchin's generalized geometry
• Conifolds and Geometric Transitions
• Gauge-Gravity Dualities, Dipoles and New Non-Kahler Manifolds
• The biHermitian topological sigma model
• 2D N=(4,4) superspace supergravity and bi-projective superfields
• A topological sigma model of biKaehler geometry
• First-order supersymmetric sigma models and target space geometry
• Linearizing Generalized Kahler Geometry
• T-duality, quotients and generalized Kahler geometry
• Sigma models with off-shell N=(4,4) supersymmetry and noncommuting complex structures
• D=2 N=(2,2) Semi Chiral Vector Multiplet
• Geometric Transitions on non-Kaehler Manifolds
• Black hole entropy and topological strings on generalized CY manifolds
• BiHermitian Supersymmetric Quantum Mechanics
• Generalised HyperKaehler Manifolds in String Theory
• Unobstructed K-deformations of Generalized Complex Structures and Bihermitian Structures
• Gauged (2,2) Sigma Models and Generalized Kahler Geometry
• Topological A-Type Models with Flux
• Gravity Dual of Two-Dimensional $\mathcal{N}=(2,2{)}^{\ast }$ Supersymmetric Yang-Mills Theory and Integrable Models
• Gauge-fixing Condition on Prepotential of Chiral Multiplet for Nongeometric Backgrounds
• An Alternative Topological Field Theory of Generalized Complex Geometry
• Tensionless Strings and Supersymmetric Sigma Models: Aspects of the Target Space Geometry
• Supersymmetric Sigma Model geometry
• From generalized Kaehler to generalized Sasakian structures
• Supersymmetric Poisson and Poisson-supersymmetric sigma models