The structure of N=2 supersymmetric nonlinear sigma models in AdS_4

Abstract

We present a detailed study of the most general N=2 supersymmetric sigma models in four-dimensional anti-de Sitter space AdS_4 formulated in terms of N=1 chiral superfields. The target space is demonstrated to be a non-compact hyperkahler manifold restricted to possess a special Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures and necessarily leaves one of them invariant. All hyperkahler cones, that is the target spaces of N=2 superconformal sigma models, prove to possess such a vector field that belongs to the Lie algebra of an isometry group SU(2) acting by rotations on the complex structures. A unique property of the N=2 sigma models constructed is that the algebra of OSp(2|4) transformations closes off the mass shell. We uncover the underlying N=2 superfield formulation for the N=2 sigma models constructed and compute the associated N=2 supercurrent. We give a special analysis of the most general systems of self-interacting N=2 tensor multiplets in AdS_4 and their dual sigma models realized in terms of N=1 chiral multiplets. We also briefly discuss the relationship between our results on N=2 supersymmetric sigma models formulated in the N=1 AdS superspace and the off-shell sigma models constructed in the N=2 AdS superspace in arXiv:0807.3368.

84 pages; v2: typos corrected, version published in JHEP

References in corpus (12)

• Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity
• 4D N = 2 Supergravity and Projective Superspace
• On conformal supergravity and projective superspace
• On superconformal projective hypermultiplets
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Variant supercurrent multiplets
• N=2 supergravity and supercurrents
• Variant supercurrents and Noether procedure
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics
• Chiral formulation for hyperkaehler sigma-models on cotangent bundles of symmetric spaces
• Conserved supercurrents and Fayet-Iliopoulos terms in supergravity

Cited by in corpus (21)

• Three-dimensional N=2 (AdS) supergravity and associated supercurrents
• Rigid supersymmetric theories in 4d Riemannian space
• Three-dimensional (p,q) AdS superspaces and matter couplings
• Six-dimensional Supergravity and Projective Superfields
• Three-dimensional N=2 supergravity theories: From superspace to components
• Rigidly Supersymmetric Gauge Theories on Curved Superspace
• Higher spin supercurrents in anti-de Sitter space
• Symmetries of curved superspace in five dimensions
• Symmetries of curved superspace
• Rigid 4D N=2 supersymmetric backgrounds and actions
• 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
• Vector-tensor supermultiplets in AdS and supergravity
• Field theories with (2,0) AdS supersymmetry in $\mathcal{N}=1$ AdS superspace
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$
• Isometries, gaugings and N=2 supergravity decoupling
• $\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace
• Self-dual supersymmetric nonlinear sigma models
• Higher-spin gauge models with (1,1) supersymmetry in AdS${}_3$: Reduction to (1,0) superspace
• Modeling Dark Matter Halos with Nonlinear Field Theories