On the Non-Local Obstruction to Interacting Higher Spins in Flat Space

TL;DR

The paper analyzes locality constraints for interacting higher-spin fields in flat space using the Noether procedure and current-exchange decompositions, focusing on quartic amplitudes with one high-spin leg. It demonstrates that $1/\Box$ non-local obstructions arise and cannot be universally canceled by tuning couplings or spectra under reasonable convergence assumptions, though selective cancellations occur in the gravity/singlet sector (notably with Metsaev's cubic couplings). The light-cone analysis reproduces these obstructions and finds no extra structures that would remove them beyond covariant results. Overall, the work strengthens the case that fully local interacting higher-spin theories in flat space face fundamental non-local obstructions unless additional (perhaps infinite) structures or nonlocalities are admitted.

Abstract

Owing to a renewed interest in flat space higher spin gauge theories, in this note we provide further details and clarifications on the results presented in arXiv:1107.5843 and arXiv: 1209.5755, which investigated their locality properties. Focusing, for simplicity, on quartic amplitudes with one of the external legs having non-zero integer spin (which can be considered as a prototype for Weinberg-type arguments), we review the appearance of $1/\Box$ non-localities. In particular, we emphasise that it appears to be not possible to eliminate all of the aforementioned non-localities with a judicious choice of coupling constants and spectrum. We also discuss the light-cone gauge fixing in $d=4$, and argue that the non-local obstruction discussed in the covariant language cannot be avoided using light-cone gauge formalism.