Cubic interaction for higher spins in AdSd+1 space in the explicit covariant form

Abstract

We present a slightly modified prescription of the radial pullback formalism proposed previously by R. Manvelyan, R. Mkrtchyan and W. Rühl 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 AdSd+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 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 AdSd+1 space. Nontrivial solutions of recurrence relations lead to the possibility to obtain the full set of AdSd+1 dimensional interacting terms with all curvature corrections including trace and divergence terms from any interaction term in d+2 dimensional flat space.