Abstract
The most general class of 4D mathcal{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 [1]. Here we provide the complete actions to all orders in the fermion fields. They rely upon a new mathcal{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 Poincaré supergravity are briefly discussed.
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