Radial reduction and cubic interaction for higher spins in (A)dS space

We present a new version of the radial reduction formalism to obtain a cubic interaction of higher spin gauge fields in AdSd+1 space from the corresponding cubic interaction in a flat (d+2)-dimensional background. We modify the radial reduction procedure proposed previously by T. Biswas and W. Siegel in 2002 [54] and applied to the free higher spin Lagrangian by K. Hallowell and A. Waldron in 2005 [55]. This modified radial reduction scheme is applied to interacting massless higher spin fields in Fronsdalʼs formulation, and all results are expressed in a direct AdSd+1 invariant way with AdS covariant derivatives. We present a consistent algorithm and define new procedure to obtain all corrections proportional to powers of the cosmological constant, and apply these to the main term of the cubic self-interaction.