  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.

High Energy Physics - Theory