For equal-spin currents up to spin four, conserved three-point correlators can be constructed explicitly as linear combinations of products of spin-one and spin-two Osborn-Petkou building blocks.
Cubic Interaction for Higher Spins in $AdS_{d+1}$ space in the explicit covariant form
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abstract
We present a slightly modified prescription of the radial pullback formalism proposed previously by R. Manvelyan, R. Mkrtchyan and W. R\"uhl in 2012, where authors investigated possibility to connect the main term of higher spin interaction in flat $d+2$ dimensional space to the main term of interaction in $AdS_{d+1}$ space ignoring all trace and divergent terms but expressed directly through the $AdS$ covariant derivatives and including some curvature corrections. In this paper we succeeded to solve all necessary \emph{recurrence relations} to finalize full radial pullback of the main term of cubic self-interaction for higher spin gauge fields in Fronsdal's formulation from flat to one dimension less $AdS_{d+1}$ space. Nontrivial solutions of recurrence relations lead to the possibility to obtain the full set of $AdS_{d+1}$ dimensional interacting terms with all curvature corrections including trace and divergence terms from any interaction term in $d+2$ dimensional flat space.
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Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins
For equal-spin currents up to spin four, conserved three-point correlators can be constructed explicitly as linear combinations of products of spin-one and spin-two Osborn-Petkou building blocks.