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

TL;DR

This paper introduces a new hyper-dilaton Weyl multiplet for 4D, ${\mathcal{N}}=2$ conformal supergravity, constructed via reinterpretation of hypermultiplet equations of motion, leading to a novel off-shell supergravity formulation with unique scalar and gauge field content.

Contribution

It defines a new hyper-dilaton Weyl multiplet for ${\mathcal{N}}=2$ supergravity, expanding the off-shell representations and coupling structures available in the theory.

Findings

Constructed a 24+24 off-shell hyper-dilaton Weyl multiplet.

Coupled the multiplet to a vector multiplet to recover known supergravity multiplets.

Discovered a scalar potential for the dilaton induced by a $BF$-coupling without standard gauging.

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 ${\mathcal{N}}=2$ Poincar\'e supergravity constructed by M\"uller in 1986. On-shell, this contains the minimal ${\mathcal{N}}=2$ Poincar\'e 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.