Super-Weyl invariance in 5D supergravity

TL;DR

This paper develops a superspace formulation for 5D N=1 conformal supergravity, introducing super-Weyl invariance, new off-shell supermultiplets, and a super-Weyl invariant action principle, enriching the geometric and matter coupling framework.

Contribution

It introduces a superspace approach to 5D conformal supergravity with super-Weyl invariance and new off-shell supermultiplets, expanding the superconformal tensor calculus.

Findings

Superspace constraints are invariant under super-Weyl transformations.

A large family of off-shell supermultiplets with super-Weyl laws is identified.

A super-Weyl invariant action principle is formulated.

Abstract

We propose a superspace formulation for the Weyl multiplet of N=1 conformal supergravity in five dimensions. The corresponding superspace constraints are invariant under super-Weyl transformations generated by a real scalar parameter. The minimal supergravity multiplet, which was introduced by Howe in 1981, emerges if one couples the Weyl multiplet to an Abelian vector multiplet and then breaks the super-Weyl invariance by imposing the gauge condition W=1, with W the field strength of the vector multiplet. The geometry of superspace is shown to allow the existence of a large family of off-shell supermultiplets that possess uniquely determined super-Weyl transformation laws and can be used to describe supersymmetric matter. Many of these supermultiplets have not appeared within the superconformal tensor calculus. We formulate a manifestly locally supersymmetric and super-Weyl invariant action principle. In the super-Weyl gauge W=1, this action reduces to that constructed in arXiv:0712.3102. We also present a superspace formulation for the dilaton Weyl multiplet.