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

Abstract

AbstractIn 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 describing a complex scalar field φ coupled to an infinite set of background CHS fields h, with possessing a non‐abelian gauge symmetry. Two characteristic features of the perturbative constructions of 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) is defined on an arbitrary conformally‐flat background; and (ii) the background conformal symmetry is manifestly realised. Next, our results are extended to the supersymmetric case. Specifically, we construct, for the first time, a model for a conformal scalar/chiral multiplet Φ 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) is defined on an arbitrary conformally‐flat superspace background; and (ii) the background superconformal symmetry is manifest. Making use of , an interacting superconformal higher‐spin theory can be defined as an induced action.