Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space

TL;DR

This paper introduces a modified radial reduction method to derive cubic interactions for higher spin gauge fields in (A)dS space from flat space interactions, ensuring $AdS$ invariance and including cosmological constant corrections.

Contribution

It develops a new radial reduction scheme for higher spin interactions in (A)dS space, extending previous methods and providing a systematic way to incorporate cosmological constant effects.

Findings

Derived cubic interactions in (A)dS space from flat space models.

Expressed results in an $AdS_{d+1}$ invariant form with covariant derivatives.

Provided an algorithm for including cosmological constant corrections.

Abstract

We present a new version of the radial reduction formalism to obtain a cubic interaction of higher spin gauge fields in $AdS_{d+1}$ 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 and applied to the free higher spin Lagrangian by K. Hallowell and A. Waldron in 2005. This modified radial reduction scheme is applied to interacting massless higher spin fields in Fronsdal's formulation, and all results are expressed in a direct $AdS_{d+1}$ 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.