Higher-Spin Interactions: four-point functions and beyond

TL;DR

This paper constructs an infinite class of gauge-invariant four-point functions for massless higher-spin fields in flat space, revealing their non-local interactions and connections to string theory features.

Contribution

It introduces a new class of higher-spin four-point functions consistent with gauge symmetry, highlighting non-local couplings and extending to n-point functions and mixed fields.

Findings

Constructed gauge-invariant four-point functions for higher-spin fields.

Revealed non-local nature of higher-spin interactions.

Connected higher-spin theories with string theory properties.

Abstract

In this work we construct an infinite class of four-point functions for massless higher-spin fields in flat space that are consistent with the gauge symmetry. In the Lagrangian picture, these reflect themselves in a peculiar non-local nature of the corresponding non-abelian higher-spin couplings implied by the Noether procedure that starts from the fourth order. We also comment on the nature of the colored spin-2 excitation present both in the open string spectrum and in the Vasiliev system, highlighting how some aspects of String Theory appear to reflect key properties of Field Theory that go beyond its low energy limit. A generalization of these results to n-point functions, fermions and mixed-symmetry fields is also addressed.