A new approach to curved projective superspace

TL;DR

This paper introduces a novel formulation of curved projective superspace for 4D N=2 supergravity, utilizing an auxiliary SU(2) manifold to simplify the geometric structure and facilitate action principle construction.

Contribution

It develops a new curved projective superspace framework with an auxiliary SU(2) manifold, enabling easier gauge fixing and component reduction for 4D N=2 supergravity.

Findings

Formulation extends 4D N=2 superspace with an auxiliary SU(2) manifold.

Introduces a projective superspace action principle in an analytic subspace.

Provides a component reduction via a five-form on spacetime and a contour in SU(2).

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.