Quartet unconstrained formulation for massless higher spin fields

TL;DR

This paper develops a straightforward, unconstrained Lagrangian framework for massless higher spin fields in flat and anti de Sitter spaces, simplifying their theoretical description and ensuring gauge invariance.

Contribution

It introduces a quartet field formulation that describes irreducible massless higher spin fields without constraints, improving on previous triplet models.

Findings

The formulation is local and free of higher derivatives.

It applies efficiently to massless higher spin fermions in anti de Sitter space.

The approach connects with the universal BRST method.

Abstract

We construct simple unconstrained Lagrangian formulations for massless higher spin fields in flat space of arbitrary dimension and on anti de Sitter background. Starting from the triplet equations of Francia and Sagnotti, which describe a chain of spin modes, we introduce an auxiliary field and find appropriate gauge invariant constraints that single out the spin-s mode. The resulting quartet of fields, thus describing an irreducible representation of the Poincare group, is used to construct simple Lagrangian formulations, which are local, free from higher derivative terms and use equal number of auxiliary fields for an unconstrained description of any value of spin. Our method proves to be most efficient for an unconstrained description of massless higher spin fermions in anti de Sitter space. A relation of the minimal models with the universal BRST approach is discussed.