Hyper-dilaton Weyl multiplet of 4D, $$ \mathcal{N} $$ = 2 conformal supergravity

Abstract

We define a new dilaton Weyl multiplet of $$ \mathcal{N} $$ N = 2 conformal supergravity in four dimensions. This is constructed by reinterpreting the equations of motion of an on-shell hypermultiplet as constraints that render some of the fields of the standard Weyl multiplet composite. The independent bosonic components include four scalar fields and a triplet of gauge two-forms. The resulting, so-called, hyper-dilaton Weyl multiplet defines a 24 + 24 off-shell representation of the local $$ \mathcal{N} $$ N = 2 superconformal algebra. By coupling the hyper-dilaton Weyl multiplet to an off-shell vector multiplet compensator, we obtain one of the two minimal 32 + 32 off-shell multiplets of $$ \mathcal{N} $$ N = 2 Poincaré supergravity constructed by Müller in 1986. On-shell, this contains the minimal $$ \mathcal{N} $$ N = 2 Poincaré supergravity multiplet together with a hypermultiplet where one of its physical scalars plays the role of a dilaton, while its three other scalars are dualised to a triplet of real gauge two-forms. Interestingly, a BF-coupling induces a scalar potential for the dilaton without a standard gauging.