Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations

Abstract

New homotopy approach to the analysis of nonlinear higher-spin equations is developed. It is shown to directly reproduce the previously obtained local vertices. Simplest cubic (quartic in Lagrangian nomenclature) higher-spin interaction vertices in four dimensional theory are examined from locality perspective by the new approach and shown to be local. The results are obtained in a background independent fashion.

arXiv comment29 pages, minor typos in eqs. (4.56) and (4.57) corrected

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• Manifest Form of the Spin-Local Higher-Spin Vertex ${{\rm Y}}_{\omega CCC}^{\eta \eta }$
• Planar solutions of higher-spin theory. Nonlinear corrections
• Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT
• Planar solutions of higher-spin theory I: free field level
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Higher spin fluctuations on spinless 4D BTZ black hole
• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• On $z$-dominance, shift symmetry and spin locality in higher-spin theory
• Higher-spin gauge theories in three spacetime dimensions
• Higher-spin gravity's "string": new gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Disentanglement of Topological and Dynamical Fields in 3d Higher-Spin Theory within Shifted Homotopy Approach
• Linearized Coxeter Higher-Spin Theories
• New diagrammatic framework for higher-spin gravity
• Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in Arbitrary Higher-Spin Background
• Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
• Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories