On conformal supergravity and projective superspace

Abstract

The projective superspace formulation for four-dimensional N = 2 matter-coupled supergravity presented in arXiv:0805.4683 makes use of the variant superspace realization for the N = 2 Weyl multiplet in which the structure group is SL(2,C) x SU(2) and the super-Weyl transformations are generated by a covariantly chiral parameter. An extension to Howe's realization of N = 2 conformal supergravity in which the tangent space group is SL(2,C) x U(2) and the super-Weyl transformations are generated by a real unconstrained parameter was briefly sketched. Here we give the explicit details of the extension.

17 pages, no figure; V2: comments and references added, published version

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• N=2 Conformal Superspace in Four Dimensions
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• Three-dimensional (p,q) AdS superspaces and matter couplings
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Six-dimensional Supergravity and Projective Superfields
• N=2 supergravity and supercurrents
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• Component reduction in N=2 supergravity: the vector, tensor, and vector-tensor multiplets
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• Lectures on nonlinear sigma-models in projective superspace
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• 2D N=(4,4) superspace supergravity and bi-projective superfields
• Extended supersymmetric sigma models in AdS_4 from projective superspace
• Goldstino superfields in N=2 supergravity
• Extended superconformal higher-spin gauge theories in four dimensions
• The linear multiplet and ectoplasm
• A new approach to curved projective superspace
• Nonlinear self-duality in N = 2 supergravity
• Supergravity-matter actions in three dimensions and Chern-Simons terms
• Superconformal geometries and local twistors
• Symmetries of supergravity backgrounds and supersymmetric field theory
• On conformal supergravity and harmonic superspace
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• New higher derivative action for tensor multiplet in N=2 conformal supergravity in four dimensions
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• On 2D N=(4,4) superspace supergravity
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• Chiral supergravity actions and superforms
• Conformal interactions between matter and higher-spin (super)fields
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• New Fayet-Iliopoulos terms in $\mathcal{N}=2$ supergravity
• New superconformal multiplets and higher derivative invariants in six dimensions
• Superforms in Simple Six-dimensional Superspace
• Embedding formalism for $\mathcal{N}$-extended AdS superspace in four dimensions
• Vector-tensor supermultiplets in AdS and supergravity
• The anti-de Sitter supergeometry revisited
• New supersymmetric sigma-model duality
• Symmetries of $\mathcal{N}=(1,0)$ supergravity backgrounds in six dimensions
• Local supertwistors and conformal supergravity in six dimensions
• Partial $\mathcal{N}=2$ Supersymmetry Breaking and Deformed Hypermultiplets
• $\mathcal{N}=2$ super Yang-Mills theory in Projective Superspace
• Variant vector-tensor multiplets in supergravity: Classification and component reduction
• Relaxed hypermultiplet in four dimensional N=2 conformal supergravity
• Goldstino superfields in supergravity
• Supersymmetric Sigma Model geometry
• Generating higher-derivative couplings in N=2 supergravity
• Hyper-Dilaton Weyl Multiplet of 4D, $\mathcal{N}=2$ Conformal Supergravity