Conformal interactions between matter and higher-spin (super)fields

TL;DR

This paper develops a new approach to conformal higher-spin theories, making conformal symmetry manifest on arbitrary backgrounds and extending the framework to supersymmetric cases, enabling the construction of interacting superconformal higher-spin models.

Contribution

It provides a novel derivation of the conformal higher-spin action on conformally-flat backgrounds and introduces the first supersymmetric extension with manifest superconformal symmetry.

Findings

Derived a conformally invariant action on arbitrary conformally-flat backgrounds.

Extended the framework to include $ ext{N}=1$ supersymmetry with manifest superconformal symmetry.

Established a foundation for constructing interacting superconformal higher-spin theories.

Abstract

In even spacetime dimensions, the interacting bosonic conformal higher-spin (CHS) theory can be realised as an induced action. The main ingredient in this definition is the model $\mathcal{S}[\varphi,h]$ describing a complex scalar field $\varphi$ coupled to an infinite set of background CHS fields $h$, with $\mathcal{S}[\varphi,h]$ possessing a non-abelian gauge symmetry. Two characteristic features of the perturbative constructions of $\mathcal{S}[\varphi , h]$ given in the literature are: (i) the background spacetime is flat; and (ii) conformal invariance is not manifest. In the present paper we provide a new derivation of this action in four dimensions such that (i) $\mathcal{S}[\varphi , h]$ is defined on an arbitrary conformally-flat background; and (ii) the background conformal symmetry is manifestly realised. Next, our results are extended to the $\mathcal{N}=1$ supersymmetric case. Specifically, we construct, for the first time, a model $\mathcal{S}[\Phi, H]$ for a conformal scalar/chiral multiplet $\Phi$ coupled to an infinite set of background higher-spin superfields $H$. Our action possesses a non-abelian gauge symmetry which naturally generalises the linearised gauge transformations of conformal half-integer superspin multiplets. The other fundamental features of this model are: (i) $\mathcal{S}[\Phi, H]$ is defined on an arbitrary conformally-flat superspace background; and (ii) the background $\mathcal{N}=1$ superconformal symmetry is manifest. Making use of $\mathcal{S}[\Phi, H]$, an interacting superconformal higher-spin theory can be defined as an induced action.