$$ \mathcal{N} $$ = 4 conformal supergravity: the complete actions
Daniel Butter, Franz Ciceri, Bindusar Sahoo
Abstract
A bstract The most general class of 4D $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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.