Extended supersymmetric sigma models in AdS_4 from projective superspace

Abstract

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.

88 pages; v3: typos corrected, version published in JHEP

References in corpus (14)

• 4D N = 2 Supergravity and Projective Superspace
• On conformal supergravity and projective superspace
• On superconformal projective hypermultiplets
• Five-dimensional Superfield Supergravity
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Five-dimensional N = 1 AdS superspace: Geometry, off-shell multiplets and dynamics
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• 6D Supersymmetry, Projective Superspace and 4D, N=1 Superfields
• Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics
• On superpotentials for nonlinear sigma-models with eight supercharges
• Chiral formulation for hyperkaehler sigma-models on cotangent bundles of symmetric spaces
• New extended superconformal sigma models and Quaternion Kahler manifolds
• Vector-tensor supermultiplets in AdS and supergravity
• Comments on N = 2 supersymmetric sigma models in projective superspace

Cited by in corpus (19)

• 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
• Higher spin supercurrents in anti-de Sitter space
• Nilpotent chiral superfield in N=2 supergravity and partial rigid supersymmetry breaking
• Symmetries of curved superspace in five dimensions
• Rigid 4D N=2 supersymmetric backgrounds and actions
• Symmetries of curved superspace
• Symmetries of supergravity backgrounds and supersymmetric field theory
• Nonlinear sigma models with AdS supersymmetry in three dimensions
• Supertwistor realisations of AdS superspaces
• Supersymmetric Field Theories on AdS_p x S^q
• Embedding formalism for $\mathcal{N}$-extended AdS superspace in four dimensions
• The anti-de Sitter supergeometry revisited
• Field theories with (2,0) AdS supersymmetry in $\mathcal{N}=1$ AdS superspace
• Embedding formalism for $(p,q)$ AdS superspaces in three dimensions
• $\mathcal{N}=2$ 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