Cubic interaction vertices for massive and massless higher spin fields

TL;DR

By leveraging the light-cone formalism, this paper develops systematic methods to construct and classify cubic interaction vertices for massive and massless higher-spin fields in flat space with $d\ge 4$. It introduces harmonic and minimal schemes to derive parity-invariant (and, where applicable, parity-violating) vertices, yielding generating functions and explicit forms for both totally symmetric and mixed-symmetry fields. The work applies these methods to obtain simple Yang–Mills and gravitational couplings for massive totally symmetric fields, and provides complete vertex lists in 5d and 6d, including the ${\bf so(d-4)}$-based treatment that unifies parity sectors. These results offer a unifying, highly explicit toolkit for higher-spin cubic couplings with potential extensions to AdS, fermionic sectors, and all-orders constructions in related theories.

Abstract

Using the light-cone formulation of relativistic dynamics, we develop various methods for constructing cubic interaction vertices and apply these methods to the study of higher spin fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for massive and massless higher spin fields of arbitrary symmetry are obtained. We derive restrictions on the allowed values of spins and the number of derivatives, which provide a classification of cubic interaction vertices for totally symmetric fields. As an example of application of the light-cone formalism, we obtain simple expressions for the minimal Yang-Mills and gravitational interactions of massive totally symmetric arbitrary spin fields. We give the complete list of parity invariant and parity violating cubic interaction vertices that can be constructed for massless fields in five and six-dimensional spaces.