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

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 $\mathcal{S}[\phi ,h]$ describing a complex scalar field $\phi$ coupled to an infinite set of background CHS fields $h$, with $\mathcal{S}[\phi ,h]$ possessing a non-abelian gauge symmetry. Two characteristic features of the perturbative constructions of $\mathcal{S}[\phi ,h]$ 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) $\mathcal{S}[\phi ,h]$ 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.

arXiv comment69 pages; V2: References and new comments added, typos corrected; V3: Published version

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• $\mathcal{N}=2$ higher spins: superfield equations of motion, the hypermultiplet supercurrents, and the component structure
• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• On higher-spin $\mathcal{N}=2$ supercurrent multiplets
• Induced action for superconformal higher-spin multiplets using SCFT techniques
• $\mathcal{N}=2$ higher-spin theories and harmonic superspace
• Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins