Cubic Interaction for Higher Spins in $AdS_{d+1}$ space in the explicit covariant form

TL;DR

This paper refines a formalism to derive the full cubic interaction terms for higher spin gauge fields in AdS space from flat space, including all curvature, trace, and divergence corrections, via solving recurrence relations.

Contribution

It provides a complete solution to recurrence relations enabling the derivation of full AdS cubic interactions from flat space, extending previous approximations.

Findings

Successfully solved recurrence relations for cubic interactions.

Derived full AdS interaction terms including curvature, trace, and divergence corrections.

Established a method to connect flat space interactions to AdS space for higher spins.

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.