Homotopy Operators and Locality Theorems in Higher-Spin Equations

Abstract

A new class of shifted homotopy operators in higher-spin gauge theory is introduced. A sufficient condition for locality of dynamical equations is formulated and Pfaffian Locality Theorem identifying a subclass of shifted homotopies that decrease the degree of non-locality in higher orders of the perturbative expansion is proven.

22 pages, no figures; V3: Some normalizations changed to conform to 1807.00001, acknowledgement added; V4: 20 pages. Matches the published version. Clarifications and reference added. Section 7 is removed in favor of a more detailed future publication

References in corpus (3)

• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Test of the local form of higher-spin equations via AdS/CFT
• Lorentz covariant form of extended higher-spin equations

Cited by in corpus (19)

• Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations
• Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality
• Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes
• On holomorphic sector of higher-spin theory
• Spin-Locality of ${\eta }^2$ and ${\bar{\eta }}^2$ Quartic Higher-Spin Vertices
• Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in Higher-Spin Theory
• 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
• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• On $z$-dominance, shift symmetry and spin locality in higher-spin theory
• Homotopy Algebras in Higher Spin Theory
• Lorentz covariant form of extended higher-spin equations
• Disentanglement of Topological and Dynamical Fields in 3d Higher-Spin Theory within Shifted Homotopy Approach
• 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
• On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity