Lagrangian formulations for Bose and Fermi higher-spin fields of mixed symmetry

TL;DR

This paper reviews the construction of local Lagrangians and field equations for free bosonic and fermionic higher-spin gauge fields with mixed symmetry, focusing on eliminating trace constraints through auxiliary fields.

Contribution

It introduces a systematic approach to remove trace constraints in mixed symmetry higher-spin fields using auxiliary fields, enhancing the formulation of their Lagrangians and equations.

Findings

Unified Lagrangian formulations for bosonic and fermionic fields.

Elimination of trace constraints via auxiliary fields.

Framework applicable to flat space higher-spin theories.

Abstract

We review the structure of local Lagrangians and field equations for free bosonic and fermionic gauge fields of mixed symmetry in flat space. These are first presented in a constrained setting and then the ($\g$-)trace constraints on fields and gauge parameters are eliminated via the introduction of a number of auxiliary fields.