$N=2$ dilaton Weyl multiplet in 4D supergravity

TL;DR

This paper constructs a new variant of the $N=2$ conformal supergravity multiplet in four dimensions, called the dilaton Weyl multiplet, by eliminating auxiliary fields from an on-shell vector multiplet coupled to the standard Weyl multiplet.

Contribution

It introduces the dilaton Weyl multiplet for $N=2$ conformal supergravity in 4D, providing a novel formulation that includes gauge vectors and a two-form, and relates it to existing supergravity multiplets.

Findings

The dilaton Weyl multiplet contains 24+24 components.

It includes two gauge vectors and a gauge two-form.

It is embedded in the minimal 32+32 Poincare supergravity multiplet.

Abstract

We construct the dilaton Weyl multiplet for $N=2$ conformal supergravity in four dimensions. Beginning from an on-shell vector multiplet coupled to the standard Weyl multiplet, the equations of motion can be used to eliminate the supergravity auxiliary fields, following a similar pattern as in five and six dimensions. The resulting 24+24 component multiplet includes two gauge vectors and a gauge two-form and provides a variant formulation of $N=2$ conformal supergravity. We also show how this dilaton Weyl multiplet is contained in the minimal 32+32 Poincare supergravity multiplet introduced by Muller in superspace.