On conformal supergravity and harmonic superspace

Abstract

This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold M^{4|8} by the tangent bundle of CP^1. The resulting superspace M^{4|8} x TCP^1 can be identified in a certain gauge with the conventional harmonic superspace M^{4|8} x S^2. This approach not only makes the connection to projective superspace transparent, but simplifies calculations in harmonic superspace significantly by eliminating the need to deal directly with supergravity prepotentials. As an application of the covariant approach, we derive from harmonic superspace the full component action for the sigma model of a hyperkahler cone coupled to conformal supergravity. Further applications are also sketched.

61 pages; v2: reference added, minor changes; v3: references added, minor additional comments, published version

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Cited by in corpus (7)

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• Hyper-Dilaton Weyl Multiplets of 5D and 6D Minimal Conformal Supergravity
• Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach
• $\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace
• 4D N=1 Kaluza-Klein superspace
• Relaxed hypermultiplet in four dimensional N=2 conformal supergravity
• Hyper-Dilaton Weyl Multiplet of 4D, $\mathcal{N}=2$ Conformal Supergravity