A new approach to curved projective superspace

Abstract

We present a new formulation of curved projective superspace. The 4D N=2 supermanifold M^{4|8} (four bosonic and eight Grassmann coordinates) is extended by an auxiliary SU(2) manifold, which involves introducing a vielbein and related connections on the full M^{7|8} = M^{4|8} x SU(2). Constraints are chosen so that it is always possible to return to the central gauge where the auxiliary SU(2) manifold largely decouples from the curved manifold M^{4|8} describing 4D N=2 conformal supergravity. We introduce the relevant projective superspace action principle in the analytic subspace of M^{7|8} and construct its component reduction in terms of a five-form J living on M^4 x C, with C a contour in SU(2). This approach is inspired by and generalizes the original approach taken in arXiv:0805.4683 and related works, which can be identified with a complexified version of the central gauge of the formulation presented here.

46 pages; v4: version to be submitted to JHEP

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• New Fayet-Iliopoulos terms in $\mathcal{N}=2$ supergravity
• Symmetries of $\mathcal{N}=(1,0)$ supergravity backgrounds in six dimensions
• N=2 conformal supergravity in five dimensions
• Non-conformal supercurrents in six dimensions
• Hyper-Dilaton Weyl Multiplet of 4D, $\mathcal{N}=2$ Conformal Supergravity