Consistent couplings between spin-2 and spin-3 massless fields

TL;DR

This paper constructs consistent first-order interactions between massless spin-2 and spin-3 fields in flat spacetime, ensuring a non-Abelian gauge algebra while respecting key physical symmetries.

Contribution

It provides the first systematic construction of such couplings without restrictions on derivatives, maintaining locality, Poincare invariance, parity, and analyticity.

Findings

Established consistent non-Abelian couplings in arbitrary dimensions

No restrictions on the number of derivatives in the Lagrangian

Ensured compatibility with fundamental symmetries

Abstract

We solve the problem of constructing consistent first-order cross-interactions between spin-2 and spin-3 massless fields in flat spacetime of arbitrary dimension n > 3 and in such a way that the deformed gauge algebra is non-Abelian. No assumptions are made on the number of derivatives involved in the Lagrangian, except that it should be finite. Together with locality, we also impose manifest Poincare invariance, parity invariance and analyticity of the deformations in the coupling constants.