BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields

TL;DR

This paper develops a manifestly Lorentz-covariant, off-shell BRST-BV framework for cubic interaction vertices of massive and massless higher-spin fields in flat space. It provides generating functions for gauge-invariant vertices across mixed-symmetry and totally symmetric fields, and classifies the totally symmetric case by spins and derivative counts, linking to known light-cone gauge results. The construction hinges on BRST-closed linear, quadratic, and cubic oscillator forms (L, Q, Z) with two representative schemes (massive field strength and minimal derivative), yielding explicit Yang–Mills and gravitational couplings for massive totally symmetric fields. The results establish a systematic, covariant avenue to study higher-spin interactions and their AdS/flat-space extensions, with clear prescriptions for deriving covariant vertices from light-cone data.

Abstract

Using BRST-BV formulation of relativistic dynamics, we study arbitrary spin massive and massless fields propagating in flat space. Generating functions of gauge invariant off-shell cubic interaction vertices for mixed-symmetry and totally symmetric fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives, which provide a classification of cubic interaction vertices for such fields. As by product, we present simple expressions for the Yang-Mills and gravitational interactions of massive totally symmetric arbitrary spin fields.