Conformal Interactions Between Matter and Higher-Spin (Super)Fields

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 S[phi,h]$\mathcal {S}[\varphi ,h]$ describing a complex scalar field phi coupled to an infinite set of background CHS fields h, with S[phi,h]$\mathcal {S}[\varphi ,h]$ possessing a non-abelian gauge symmetry. Two characteristic features of the perturbative constructions of S[phi,h]$\mathcal {S}[\varphi , h]$ 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) S[phi,h]$\mathcal {S}[\varphi , h]$ is defined on an arbitrary conformally-flat background; and (ii) the background conformal symmetry is manifestly realised. Next, our results are extended to the N=1$\mathcal {N}=1$ supersymmetric case. Specifically, we construct, for the first time, a model S[phi,H]$\mathcal {S}[\Phi , H]$ 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) S[phi,H]$\mathcal {S}[\Phi , H]$ is defined on an arbitrary conformally-flat superspace background; and (ii) the background N=1$\mathcal {N}=1$ superconformal symmetry is manifest. Making use of S[phi,H]$\mathcal {S}[\Phi , H]$, an interacting superconformal higher-spin theory can be defined as an induced action.