Hyper-Dilaton Weyl Multiplet of 4D, $\mathcal{N}=2$ Conformal Supergravity

Abstract

We define a new dilaton Weyl multiplet of $\mathcal{N}=2$ 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 $\mathcal{N}=2$ 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 $\mathcal{N}=2$ Poincaré supergravity constructed by Müller in 1986. On-shell, this contains the minimal $\mathcal{N}=2$ 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.

v3: typo corrected in eq. (2.33)