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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 modelS  [  φ  ,  h  ]   $\mathcal {S}[\varphi ,h]$    describing a complex scalar field φ coupled to an infinite set of background CHS fields  h , withS  [  φ  ,  h  ]   $\mathcal {S}[\varphi ,h]$    possessing a non‐abelian gauge symmetry. Two characteristic features of the perturbative constructions ofS  [  φ  ,  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  [  φ  ,  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 theN  =  1   $\mathcal {N}=1$    supersymmetric case. Specifically, we construct, for the first time, a modelS  [  Φ  ,  H  ]   $\mathcal {S}[\Phi , H]$    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)S  [  Φ  ,  H  ]   $\mathcal {S}[\Phi , H]$    is defined on an arbitrary conformally‐flat superspace background; and (ii) the backgroundN  =  1   $\mathcal {N}=1$    superconformal symmetry is manifest. Making use ofS  [  Φ  ,  H  ]   $\mathcal {S}[\Phi , H]$   , an interacting superconformal higher‐spin theory can be defined as an induced action.

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