BRST approach to Lagrangian construction for fermionic massless higher spin fields

TL;DR

This paper develops a BRST-based method for constructing Lagrangians for massless fermionic higher spin fields in any dimension, revealing their gauge structure and auxiliary fields, and providing explicit formulations including for spin 5/2.

Contribution

It introduces a general BRST approach for fermionic higher spin fields, accommodating arbitrary spins without off-shell constraints, and derives new Lagrangians with extended gauge symmetries.

Findings

The model is a reducible gauge theory with complexity increasing with spin.

In 4D, the Lagrangian reduces to Fang-Fronsdal form after gauge fixing.

A new Lagrangian for spin 5/2 fields with auxiliary fields is derived.

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.