Generalised connections and higher-spin equations

Abstract

We consider high-derivative equations obtained setting to zero the divergence of the higher-spin curvatures in metric-like form, showing their equivalence to the second-order equations emerging from the tensionless limit of open string field theory, which propagate reducible spectra of particles with different spins. This result can be viewed as complementary to the possibility of setting to zero a single trace of the higher-spin field strengths, which yields an equation known to imply Fronsdal's equation in the compensator form. Higher traces and divergences of the curvatures produce a whole pattern of high-derivative equations whose systematics is also presented.

12 pages, minor changes

References in corpus (23)

• On higher spins and the tensionless limit of String Theory
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Tensor gauge fields in arbitrary representations of GL(D,R) : duality & Poincare lemma
• Free geometric equations for higher spins
• On the geometry of higher-spin gauge fields
• On geometric equations and duality for free higher spins
• Current Exchanges and Unconstrained Higher Spins
• Tensor fields of mixed Young symmetry type and N-complexes
• Description of the higher massless irreducible integer spins in the BRST approach
• Minimal Local Lagrangians for Higher-Spin Geometry
• Quartet unconstrained formulation for massless higher spin fields
• Constant Curvature Algebras and Higher Spin Action Generating Functions
• Higher-Spin Geometry and String Theory
• Massless Poincare modules and gauge invariant equations
• Geometric Lagrangians for massive higher-spin fields
• String theory triplets and higher-spin curvatures
• Transverse Invariant Higher Spin Fields
• A note on higher-derivative actions for free higher-spin fields
• On the relation between local and geometric Lagrangians for higher spins
• Low-spin models for higher-spin Lagrangians
• Geometric massive higher spins and current exchanges
• On Nonlinear Higher Spin Curvature
• Lagrangian higher spin field theories from the O(N) extended supersymmetric particle

Cited by in corpus (21)

• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Elements of Vasiliev theory
• Classical and quantum stability of higher-derivative dynamics
• Cubic interactions of Maxwell-like higher spins
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Continuous spin fields of mixed-symmetry type
• A note on higher-derivative actions for free higher-spin fields
• On asymptotic symmetries in higher dimensions for any spin
• Massless Scalars and Higher-Spin BMS in Any Dimension
• On the Lagrangian formulation of the double copy to cubic order
• Multi-Hamiltonian formulations and stability of higher-derivative extensions of $3d$ Chern-Simons
• Supersymmetric Reducible Higher-Spin Multiplets in Various 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
• One-loop effective actions and higher spins. II
• Higher-derivative massive actions from dimensional reduction
• Fermionic higher-spin triplets in AdS
• A connection between linearized Gauss-Bonnet gravity and classical electrodynamics II: Complete dual formulation
• U(N) spinning particles and higher spin fields on Kaehler backgrounds
• Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities