On Killing tensors and cubic vertices in higher-spin gauge theories

Abstract

The problem of determining all consistent non-Abelian local interactions is reviewed in flat space-time. The antifield-BRST formulation of the free theory is an efficient tool to address this problem. Firstly, it allows to compute all on-shell local Killing tensor fields, which are important because of their deep relationship with higher-spin algebras. Secondly, under the sole assumptions of locality and Poincare invariance, all non-trivial consistent deformations of a sum of spin-three quadratic actions deforming the Abelian gauge algebra were determined. They are compared with lower-spin cases.

10 pages. Based on a talk given by X.B. at the RTN Workshop ``Constituents, Fundamental Forces and Symmetries of the Universe'' (Corfu, 20-26th September 2005). Contribution to the Proceedings

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• Current Exchanges and Unconstrained Higher Spins
• Higher-Spin Interactions: four-point functions and beyond
• Higher-Spin Gauge Theories and Bulk Locality
• Universal Limits on Massless High-Spin Particles
• Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields
• Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields
• Consistent couplings between spin-2 and spin-3 massless fields
• Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex
• Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space
• Spin 3 cubic vertices in a frame-like formalism
• Exploring the S-Matrix of Massless Particles
• Cubic interactions of Maxwell-like higher spins
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• Unconstrained Higher Spins of Mixed Symmetry. II. Fermi Fields
• Direct construction of a cubic selfinteraction for higher spin gauge fields
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Off-shell construction of some trilinear higher spin gauge field interactions
• Cubic interaction vertex of higher-spin fields with external electromagnetic field
• Notes on higher-spin algebras: minimal representations and structure constants
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space
• Comments on higher-spin symmetries
• Structure of Higher Spin Gauge Interactions
• Cubic-interaction-induced deformations of higher-spin symmetries
• Cubic Interaction for Higher Spins in $Ad{S}_{d+1}$ space in the explicit covariant form
• Restrictions for $n$-Point Vertices in Higher-Spin Theories
• Hierarchy of Supersymmetric Higher Spin Connections
• Scattering of charged tensor bosons in gauge and superstring theories
• Superspace First Order Formalism, Trivial Symmetries and Electromagnetic Interactions of Linearized Supergravity
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins