N=4 conformal supergravity: the complete actions

TL;DR

This paper presents the complete four-dimensional N=4 conformal supergravity actions, including all fermionic terms, based on a new density formula, advancing the understanding of supergravity theories and their applications.

Contribution

It provides the full off-shell actions for N=4 conformal supergravity, extending previous bosonic results with a novel density formula that includes fermionic contributions.

Findings

Complete N=4 conformal supergravity actions to all fermion orders.

New density formula enabling direct construction of supergravity actions.

Application to vector multiplets and Poincaré supergravity contexts.

Abstract

The most general class of 4D N=4 conformal supergravity actions depends on a holomorphic function of the scalar fields that parametrize an SU(1,1)/U(1) coset space. The bosonic sector of these actions was presented in a letter [arXiv:1609.09083]. Here we provide the complete actions to all orders in the fermion fields. They rely upon a new N=4 density formula, which permits a direct but involved construction. This density formula also recovers the on-shell action for vector multiplets coupled to conformal supergravity. Applications of these results in the context of Poincar\'e supergravity are briefly discussed.