Metric-like Lagrangian Formulations for Higher-Spin Fields of Mixed Symmetry

TL;DR

This paper reviews the development of local Lagrangian formulations for free mixed-symmetry higher-spin fields, highlighting the elimination of constraints and the emergence of Weyl-like symmetries in specific models.

Contribution

It introduces unconstrained metric-like Lagrangian formulations for mixed-symmetry higher-spin fields, extending previous constrained approaches and revealing new symmetries.

Findings

Elimination of trace constraints via auxiliary fields

Identification of Weyl-like symmetries in certain models

Extension of metric formulation to mixed-symmetry fields

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 extending the metric formulation of linearized gravity, and then the ($\gamma$-)trace constraints on fields and gauge parameters are eliminated via the introduction of auxiliary fields. We also display the emergence of Weyl-like symmetries in particular classes of models in low space-time dimensions.