N = 2 supersymmetric sigma-models and duality

Abstract

For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear sigma-models constructed originally in projective superspace, we develop their formulation in terms of N = 1 chiral superfields. Specifically, these theories are: (i) sigma-models on cotangent bundles T*M of arbitrary real analytic Kaehler manifolds M; (ii) general superconformal sigma-models described by weight-one polar supermultiplets. Using superspace techniques, we obtain a universal expression for the holomorphic symplectic two-form ω^{(2,0)} which determines the second supersymmetry transformation and is associated with the two complex structures of the hyperkaehler space T*M that are complimentary to the one induced from M. This two-form is shown to coincide with the canonical holomorphic symplectic structure. In the case (ii), we demonstrate that ω^{(2,0)} and the homothetic conformal Killing vector determine the explicit form of the superconformal transformations. At the heart of our construction is the duality (generalized Legendre transform) between off-shell N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral realizations. We finally present the most general N = 2 superconformal nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The approach developed can naturally be generalized in order to describe 5D and 6D superconformal nonlinear sigma-models in 4D N = 1 superspace.

31 pages, no figures; V2: reference and comments added, typos corrected; V3: more typos corrected, published version

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Cited by in corpus (14)

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• Off-shell superconformal nonlinear sigma-models in three dimensions
• N=2 supersymmetric sigma-models in AdS
• Lectures on nonlinear sigma-models in projective superspace
• The structure of N=2 supersymmetric nonlinear sigma models in AdS_4
• Extended supersymmetric sigma models in AdS_4 from projective superspace
• Symmetries of supergravity backgrounds and supersymmetric field theory
• Nonlinear sigma models with AdS supersymmetry in three dimensions
• Metastable supersymmetry breaking in N=2 non-linear sigma-models
• Relating harmonic and projective descriptions of N=2 nonlinear sigma models
• Comments on N = 2 supersymmetric sigma models in projective superspace
• New supersymmetric sigma-model duality
• Darboux Coordinates and Instanton Corrections in Projective Superspace
• Self-dual supersymmetric nonlinear sigma models