A 24+24 real scalar multiplet in four dimensional N=2 conformal supergravity

TL;DR

This paper constructs and analyzes a new 24+24 component scalar multiplet in four-dimensional N=2 conformal supergravity, extending the understanding of supermultiplet structures and their couplings.

Contribution

It introduces a novel 24+24 scalar multiplet in N=2 conformal supergravity, derived from supercurrent multiplets, with explicit transformation laws and constraints.

Findings

Derived the transformation laws for the new multiplet in conformal supergravity.

Established the equivalence to Howe et al's flat space multiplet via field redefinition.

Presented constraints to obtain a minimal off-shell matter multiplet.

Abstract

Starting from the 48+48 component multiplet of supercurrents for a rigid N=2 tensor multiplet in four spacetime dimensions, we obtain the transformation of the linearized supergravity multiplet which couples to this supercurrent multiplet. At the linearized level, this 48+48 component supergravity multiplet decouples into the 24+24 component linearized standard Weyl multiplet and a 24+24 component irreducible matter multiplet containing a real scalar field. By a consistent application of the supersymmetry algebra with field dependent structure constants appropriate to N=2 conformal supergravity, we find the full transformation law for this multiplet in a conformal supergravity background. By performing a field redefinition and switching off the conformal supergravity background, the multiplet is equivalent to the one introduced by Howe et al in flat space as a constrained real scalar superfield. We present a set of constraints which can be consistently imposed on this multiplet to obtain a restricted minimal 8+8 off-shell matter multiplet. We also show as an example the precise embedding of the tensor multiplet inside this multiplet.