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

## TL;DR

This paper investigates the inherent non-local obstructions in constructing interacting higher spin gauge theories in flat space, showing that such non-localities cannot be fully eliminated through gauge choices or coupling adjustments.

## Contribution

It provides a detailed analysis of non-localities in flat space higher spin interactions, extending previous results and demonstrating their unavoidable nature.

## Key findings

- Non-local $1/\Box$ terms appear in quartic amplitudes.
- Non-localities cannot be removed by coupling choices.
- Light-cone gauge does not resolve non-local obstructions.

## 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.