On the gauge symmetries of Maxwell-like higher-spin Lagrangians

Abstract

In their simplest form, metric-like Lagrangians for higher-spin massless fields display constrained gauge symmetries, unless auxiliary fields are introduced or locality is foregone. Specifically, in its standard incarnation, gauge invariance of Maxwell-like Lagrangians relies on parameters with vanishing divergence. We propose an alternative form of the corresponding local symmetry involving unconstrained parameters of mixed-symmetry type, described by rectangular two-row Young diagrams and entering high-derivative gauge transformations. The resulting gauge algebra appears to be reducible and we display the full pattern of gauge-for-gauge parameters, testing its correctness via the corresponding counting of degrees of freedom. Incidentally, this shows that massless higher spins admit a local unconstrained formulation with no need for auxiliary fields.

24 pages; minor changes in the Introduction, references added. To appear in Nucl. Phys. B

References in corpus (5)

• Transverse Fierz-Pauli symmetry
• Current Exchanges and Unconstrained Higher Spins
• Geometric Lagrangians for massive higher-spin fields
• Transverse Invariant Higher Spin Fields
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields

Cited by in corpus (24)

• Elements of Vasiliev theory
• Classical and quantum stability of higher-derivative dynamics
• Cubic interactions of Maxwell-like higher spins
• Basic introduction to higher-spin theories
• On the Lagrangian formulation of the double copy to cubic order
• Cubic interactions of massless bosonic fields in three dimensions
• Supersymmetric Continuous Spin Gauge Theory
• Mixed-symmetry multiplets and higher-spin curvatures
• A local action for fermionic unconstrained higher spin gauge fields in (A)dS space
• Cubic-interaction-induced deformations of higher-spin symmetries
• A note on unfree gauge symmetry
• Constrained BRST- BFV Lagrangian formulations for Higher Spin Fields in Minkowski Spaces
• Unfree gauge symmetry in the BV formalism
• BRST-BFV and BRST-BV Descriptions for Bosonic Fields with Continuous Spin on $R^{1,d-1}$
• A Note on Vectorial AdS${}_5$/CFT${}_4$ Duality for Spin-$j$ Boundary Theory
• Unfree gauge symmetry in the Hamiltonian formalism
• Hamiltonian constraints and unfree gauge symmetry
• Gauge symmetry of unimodular gravity in Hamiltonian formalism
• Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
• Symmetric vs. chiral approaches to massive fields with spin
• Dualisation of free fields
• Multiple choice of gauge generators and consistency of interactions
• Global conserved quantities and unfree gauge symmetry
• Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities