Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in Higher-Spin Theory

Abstract

The concepts of compact and projectively-compact spin-local spinor vertices are introduced. Vertices of this type are shown to be space-time spin-local, i.e. their restriction to any finite subset of fields is space-time local. The known spinor spin-local cubic vertices with the minimal number of space-time derivatives are verified to be projectively-compact. This has the important consequence that spinor spin-locality of the respective quartic vertices would imply their space-time spin-locality. More generally, it is argued that the proper class of solutions of the non-linear higher-spin equations that leads to the minimally non-local (presumably space-time spin-local) vertices is represented by the projectively-compact vertices. The related aspects of the higher-spin holographic correspondence are briefly discussed.

arXiv comment21 pages, no figures; V2: typos and wrong reference corrected, minor comments added. Matches the published version

References in corpus (29)

• Gauge Theory Correlators from Non-Critical String Theory
• AdS Dual of the Critical O(N) Vector Model
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Massless Higher Spins and Holography
• Chern-Simons Theory with Vector Fermion Matter
• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Stringy gravity, interacting tensionless strings and massless higher spins
• Cubic interaction vertices for massive and massless higher spin fields
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• String Lessons for Higher-Spin Interactions
• Light-Front Higher-Spin Theories in Flat Space
• Cubic interaction vertices for fermionic and bosonic arbitrary spin fields
• General trilinear interaction for arbitrary even higher spin gauge fields
• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• Higher-Spin Gauge Theories and Bulk Locality
• Light-cone form of field dynamics in anti-de Sitter space-time and AdS/CFT correspondence
• Holography, Unfolding and Higher-Spin Theory
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations
• Homotopy Operators and Locality Theorems in Higher-Spin Equations
• Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations
• Test of the local form of higher-spin equations via AdS/CFT
• Moyal multiplier algebras of the test function spaces of type S
• Manifest Form of the Spin-Local Higher-Spin Vertex ${{\rm Y}}_{\omega CCC}^{\eta \eta }$
• Higher Spin Superfield interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices
• Invariant Functionals in Higher-Spin Theory
• Star-Product Functions in Higher-Spin Theory and Locality
• Unfolding, higher spins, metaplectic groups and resolution of classical singularities

Cited by in corpus (10)

• On holomorphic sector of higher-spin theory
• $\mathcal{N}=2$ higher spins: superfield equations of motion, the hypermultiplet supercurrents, and the component structure
• On $z$-dominance, shift symmetry and spin locality in higher-spin theory
• Cubic interactions of d4 irreducible massless higher spin fields within BRST approach
• Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields
• BRST-BV approach for interacting higher spin fields
• Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
• New diagrammatic framework for higher-spin gravity
• Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in Arbitrary Higher-Spin Background
• Quintic vertices of spin 3, vector and scalar fields