Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields

TL;DR

This work develops a local, metric-like unconstrained Lagrangian formalism for free bosonic higher-spin gauge fields with mixed symmetry in flat space, extending Labastida’s constrained theory. The authors introduce compensator fields and Lagrange multipliers and use Bianchi identities to build minimal unconstrained Lagrangians that reproduce Labastida’s results when constraints are enforced, while allowing higher-derivative compensator terms or, in a non-minimal variant, two-derivative dynamics. They provide a detailed two-family analysis, generalize to $N$ families, and discuss irreducible representations and current exchanges, revealing Weyl-like symmetries in sporadic low-dimensional cases. They also explore simplifying the higher-derivative structure via auxiliary compensators and extend the construction to multi-forms, outlining a path toward a comprehensive framework for mixed-symmetry fields that underpins connections to string theory. A companion paper extends the framework to fermions, aiming to complete the metric-like picture of free higher-spin fields and to pave the way for interactions and string-inspired applications.

Abstract

This is the first of two papers devoted to the local "metric-like" unconstrained Lagrangians and field equations for higher-spin gauge fields of mixed symmetry in flat space. Here we complete the previous constrained formulation of Labastida for Bose fields. We thus recover his Lagrangians via the Bianchi identities, before extending them to their "minimal" unconstrained form with higher derivatives of the compensator fields and to yet another, non-minimal, form with only two-derivative terms. We also identify classes of these systems that are invariant under Weyl-like symmetries.