BRST approach to Lagrangian construction for fermionic massless higher spin fields

TL;DR

This work develops a BRST framework for free massless fermionic higher‑spin fields in flat spacetime of arbitrary dimension, introducing an enlarged constraint algebra with auxiliary oscillators to realize irreducible, fixed‑spin representations and then extend to all half‑integer spins. It produces Lagrangians for individual spins and for the full half‑integer spectrum, revealing a reducible gauge symmetry whose order grows with spin, and demonstrates that in $D=4$ these Lagrangians reduce to the Fang–Fronsdal form after partial gauge fixing. A detailed spin‑$5/2$ example shows the explicit auxiliary‑field content and gauge structure. The approach promises extensions to mixed symmetry, AdS backgrounds, massive cases, and supersymmetric higher‑spin models.

Abstract

We develop the BRST approach to Lagrangian formulation for all massless half-integer higher spin fields on an arbitrary dimensional flat space. General procedure of Lagrangian construction describing the dynamics of fermionic field with any spin is given. It is shown that in fermionic case the higher spin field model is a reducible gauge theory and the order of reducibility grows with the value of spin. No off-shell constraints on the fields and the gauge parameters are used. We prove that in four dimensions after partial gauge fixing the Lagrangian obtained can be transformed to Fang-Fronsdal form however, in general case, it includes the auxiliary fields and possesses the more gauge symmetries in compare with Fang-Fronsdal Lagrangian. As an example of general procedure, we derive the new Lagrangian for spin 5/2 field containing all set of auxiliary fields and gauge symmetries of free fermionic higher spin field theory.