Direct construction of a cubic selfinteraction for higher spin gauge fields

TL;DR

This work presents an algorithmic Noether-based construction of cubic selfinteractions for higher spin gauge fields in flat space, delivering a complete spin-4 solution and a general leading-term prediction for even spins. The authors develop a curvature-inspired ansatz and a systematic integration-by-parts strategy to solve Noether's equation, recovering the spin-2 (gravity) case as a consistency check. The spin-4 results are explicit and shown to be consistent with the general spin-s prediction, highlighting a path toward an extended gravity framework. Overall, the paper provides a concrete Lagrangian formulation for HS self-interactions in flat space with implications for AdS/CFT and beyond.

Abstract

Using Noether's procedure we directly construct a complete cubic selfinteraction for the case of spin s=4 in a flat background and discuss the cubic selfinteraction for general spin s with s derivatives in the same background. The leading term of the latter interaction together with the leading gauge transformation of first field order are presented.