From BRST to light-cone description of higher spin gauge fields

TL;DR

This work shows how to derive the light-cone action for free higher-spin gauge fields from a BRST formulation by systematically eliminating quartets in a graded BRST setup. By reducing the BRST complex to the lowest-graded sector and applying level and trace constraints, it recovers the light-cone action and provides explicit expressions for the reduced Poincaré generators. The approach clarifies how the Fronsdal spectrum arises either with or without trace constraints, through a detailed analysis of BRST cohomology and observable reduction. The results bridge BRST and light-cone frameworks for higher-spin fields in four dimensions, offering an alternative route to analyze physical content and helicity structure of massless higher-spin actions.

Abstract

In this short note we show, at the level of action principles, how the light-cone action of higher spin gauge fields can easily be obtained from the BRST formulation through the elimination of quartets. We analyze how the algebra of cohomology classes is affected by such a reduction. By applying the reduction to the Poincare generators, we give an alternative way of analyzing the physical spectrum of the Fronsdal type actions, with or without trace condition.