Unconstrained Higher Spins of Mixed Symmetry. II. Fermi Fields

TL;DR

This paper extends the formulation of higher-spin fermionic fields with mixed symmetry by deriving unconstrained Lagrangians and equations, introducing minimal and non-minimal models, and identifying Weyl-like invariances.

Contribution

It provides the first unconstrained Lagrangian formulations for mixed-symmetry fermionic higher-spin fields, completing previous constrained models.

Findings

Derived unconstrained Lagrangians using Bianchi identities

Presented minimal and non-minimal formulations with different derivative orders

Identified Weyl-like symmetry invariances in these systems

Abstract

This paper is a sequel of arXiv:0810.4350 [hep-th], and is also devoted to the local "metric-like" unconstrained Lagrangians and field equations for higher-spin fields of mixed symmetry in flat space. Here we complete the previous constrained on-shell formulation of Labastida for Fermi fields, deriving the corresponding constrained Lagrangians both via the Bianchi identities and via the requirement of self-adjointness. We also describe two types of unconstrained Lagrangian formulations: a "minimal" one, containing higher derivatives of the compensator fields, and another non-minimal one, containing only one-derivative terms. We identify classes of these systems that are invariant under Weyl-like symmetry transformations.