Cubic interaction vertices in higher spin theories

TL;DR

This paper derives a universal formula for cubic interaction vertices in higher spin theories, showing they are powers of the Yang-Mills vertex, based solely on symmetry considerations in four-dimensional flat spacetime.

Contribution

It establishes a general relation for cubic vertices in higher spin theories, extending the understanding of their structure from symmetry principles.

Findings

Cubic vertex coefficients for spin λ are the λ-th power of the Yang-Mills coefficient.

The result applies to all λ in four-dimensional flat spacetime.

An explicit derivation is provided for the case λ=3.

Abstract

Based purely on symmetry considerations, we derive the following result: in momentum space, the coefficient of the cubic interaction vertex for a spin $\lambda$ field is equal to the corresponding Yang-Mills (spin 1) coefficient, raised to the power $\lambda$. This result is valid for all $\lambda$ for Lagrangians that contain a cubic interaction vertex of the form $\lambda$-$\lambda$-$\lambda$, in four-dimensional flat spacetime. For $\lambda=3$, we present an additional derivation of this result.