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

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 $1/\square$ 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.

22+12 pages. v2: typos corrected, references added

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