Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes

Abstract

The analysis of spin-locality of higher-spin gauge theory is formulated in terms of star-product functional classes appropriate for the $\beta \to -\infty$ limiting shifted homotopy proposed recently in arXiv:1909.04876 where all ${\omega }^2{C}^2$ higher-spin vertices were shown to be spin-local. For the $\beta \to -\infty$ limiting shifted contracting homotopy we identify the class of functions ${\mathcal{H}}^{+0}$, that do not contribute to the r.h.s. of HS field equations at a given order. A number of theorems and relations that organize analysis of the higher-spin equations are derived including extension of the Pfaffian Locality Theorem of arXiv:1805.11941 to the $\beta$-shifted contracting homotopy and the relation underlying locality of the ${\omega }^2{C}^2$ sector of higher-spin equations. Space-time interpretation of spin-locality of theories involving infinite towers of fields is proposed as the property that the theory is space-time local in terms of original constituent fields $\Phi$ and their local currents $J(\Phi )$ of all ranks. Spin-locality is argued to be a proper substitute of locality for theories with finite sets of fields for which the two concepts are equivalent.

arXiv comment51 pages, no figures; V2 minor corrections: typos fixed, clarifications and affiliation added; V3 55 pages, Section 3 extended to clarify the notions of spin-locality and ultra-locality. Matches the published version

References in corpus (20)

• AdS Dual of the Critical O(N) Vector Model
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Chern-Simons Theory with Vector Fermion Matter
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• Static BPS black hole in 4d higher-spin gauge theory
• Higher-Spin Gauge Theories and Bulk Locality
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Families of exact solutions to Vasiliev's 4D equations with spherical, cylindrical and biaxial symmetry
• Operator algebra of free conformal currents via twistors
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality
• From Coxeter Higher-Spin Theories to Strings and Tensor Models
• Homotopy Operators and Locality Theorems in Higher-Spin Equations
• Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations
• On the Local Frame in Nonlinear Higher-Spin Equations
• Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations

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• On a gauge-invariant deformation of a classical gauge-invariant theory
• Planar solutions of higher-spin theory. Nonlinear corrections
• Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Planar solutions of higher-spin theory I: free field level
• On $z$-dominance, shift symmetry and spin locality in higher-spin theory
• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• Higher-spin gravity's "string": new gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution
• Bulk locality and gauge invariance for boundary-bilocal cubic correlators in higher-spin gravity
• New diagrammatic framework for higher-spin gravity
• Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in Arbitrary Higher-Spin Background
• On gauge-invariant deformation of reducible gauge theories