Description of the higher massless irreducible integer spins in the BRST approach

TL;DR

This work develops a BRST framework to describe irreducible massless higher-spin representations of the Poincaré group in arbitrary dimensions. By converting second-class constraints to first-class via auxiliary variables, the authors construct a nilpotent BRST charge with terms up to the seventh degree in ghosts and derive a BRST-invariant Lagrangian that automatically introduces auxiliary fields. Through a toy model and the full constraint system, they show how partial gauge fixing reduces the theory to Fronsdal's Lagrangian for symmetric, massless spin-$n$ fields, recovering the correct irreducible spectrum in even dimensions. The approach offers a systematic BRST path to irreducible higher-spin dynamics and hints at extensions to half-integer spins with appropriate ghost structures.

Abstract

The BRST approach is applied to the description of irreducible massless higher spins representations of the Poincare group in arbitrary dimensions. The total system of constraints in such theory includes both the first and the second class constraints. The corresponding nilpotent BRST charge contains terms up to the seventh degree in ghosts.