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Abstract
In even spacetime dimensions, the interacting bosonic conformal higherspin (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 nonabelian 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 conformallyflat 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 higherspin superfields H. Our action possesses a nonabelian gauge symmetry which naturally generalises the linearised gauge transformations of conformal halfinteger superspin multiplets. The other fundamental features of this model are: (i) S[phi,H]$\mathcal {S}[\Phi , H]$ is defined on an arbitrary conformallyflat 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 higherspin theory can be defined as an induced action.
Original language  English 

Article number  2200157 
Number of pages  31 
Journal  Fortschritte der Physik 
Volume  71 
Issue number  1 
DOIs  
Publication status  Published  Jan 2023 
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Advances in Conformal Field Theory with Extended Symmetry
Kuzenko, S., Buchbinder, E., Theisen, S. & Tseytlin, A.
1/01/20 → 31/12/23
Project: Research