5D Supergravity and Projective Superspace

TL;DR

This paper develops a comprehensive projective superspace formulation for 5D N=1 supergravity, providing solutions to Bianchi identities, describing off-shell supermultiplets, and establishing a locally supersymmetric action principle.

Contribution

It offers a complete solution to the Bianchi identities for 5D supergravity and introduces a manifestly supersymmetric action principle with projective invariance.

Findings

Complete solution to Bianchi identities for 5D supergravity

Existence of large family of off-shell supermultiplets

Invariant action principle under projective transformations

Abstract

This paper is a companion to our earlier work arXiv:0710.3440 in which the projective superspace formulation for matter-coupled simple supergravity in five dimensions was presented. For the minimal multiplet of 5D N=1 supergravity introduced by Howe in 1981, we give a complete solution of the Bianchi identities. The geometry of curved superspace is shown to allow the existence of a large family of off-shell supermultiplets that can be used to describe supersymmetric matter, including vector multiplets and hypermultiplets. We formulate a manifestly locally supersymmetric action principle. Its natural property turns out to be the invariance under so-called projective transformations of the auxiliary isotwistor variables. We then demonstrate that the projective invariance allows one to uniquely restore the action functional in a Wess-Zumino gauge. The latter action is well-suited for reducing the supergravity-matter systems to components.