A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations

Abstract

In Vasiliev's unfolded formulation of higher-spin dynamics the standard fields are embedded on-shell into covariantly constant master fields valued in Lorentz-covariant slices of the star-product algebra A of functions on the singleton phase space. Correspondingly, the harmonic expansion is taken over compact slices of A that are unitarizable in a rescaled trace-norm rather than the standard Killing norm. Motivated by the higher-derivative nature of the theory, we examine indecomposable unitarizable Harish-Chandra modules consisting of standard massless particles plus linearized runaway solutions. This extension arises naturally in the above fiber approach upon realizing compact-weight states as non-polynomial analytic functions in A.

arXiv comment80 pages, 2 figures. Minor changes: typos corrected, two footnotes and references added. To be published in JHEP

References in corpus (25)

• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Higher Spin Gauge Theories: Star-Product and AdS Space
• Nonlinear higher spin theories in various dimensions
• Gauge Invariances and Phases of Massive Higher Spins in (A)dS
• Cubic interaction vertices for massive and massless higher spin fields
• How massless are massless fields in $Ad{S}_d$
• Cubic interaction vertices for fermionic and bosonic arbitrary spin fields
• On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory
• Geometric Formulation for Partially Massless Fields
• Doubletons and 5D Higher Spin Gauge Theory
• Analysis of Higher Spin Field Equations in Four Dimensions
• An Exact Solution of 4D Higher-Spin Gauge Theory
• Consistent couplings between spin-2 and spin-3 massless fields
• On Higher Spins with a Strong Sp(2,R) Condition
• Brane Partons and Singleton Strings
• Higher Spin N=8 Supergravity
• Real Forms of Complex Higher Spin Field Equations and New Exact Solutions
• On N=1,2,4 Higher Spin Gauge Theories in Four Dimensions
• 7D Bosonic Higher Spin Theory: Symmetry Algebra and Linearized Constraints
• Shadows, currents and AdS fields
• (A)dS exchanges and partially-massless higher spins
• Parity violating vertices for spin-3 gauge fields
• Higher-spin Chern-Simons theories in odd dimensions
• Higher Symmetries of the Laplacian
• Conformal Fields in Higher Dimensions

Cited by in corpus (64)

• On the uniqueness of higher-spin symmetries in AdS and CFT
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Elements of Vasiliev theory
• Biaxially symmetric solutions to 4D higher-spin gravity
• Families of exact solutions to Vasiliev's 4D equations with spherical, cylindrical and biaxial symmetry
• Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime
• Mixed-symmetry fields in de Sitter space: a group theoretical glance
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II. Oscillator Realization
• Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space
• Higher Spin Gravity Amplitudes From Zero-form Charges
• Partially-massless higher-spin algebras and their finite-dimensional truncations
• Geometry and Observables in Vasiliev's Higher Spin Gravity
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons
• A minimal BV action for Vasiliev's four-dimensional higher spin gravity
• Flato-Fronsdal theorem for higher-order singletons
• Notes on higher-spin algebras: minimal representations and structure constants
• Towards higher-spin holography in ambient space of any dimension
• Basic introduction to higher-spin theories
• CFT adapted gauge invariant formulation of massive arbitrary spin fields in AdS
• On the Algebraic Structure of Higher-Spin Field Equations and New Exact Solutions
• Formal Higher Spin Gravities
• CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge
• Twistor space observables and quasi-amplitudes in 4D higher spin gravity
• Type-B Formal Higher Spin Gravity
• New Unfolded Higher Spin Systems in $Ad{S}_3$
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• FRW and domain walls in higher spin gravity
• Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
• Carrollian conformal scalar as flat-space singleton
• On big crunch solutions in Prokushkin-Vasiliev theory
• Towards higher-spin AdS${}_2$/CFT${}_1$ holography
• Towards higher-spin holography in flat space
• On Higher Spin Symmetries in AdS_{5}
• Fronsdal fields from gauge functions in Vasiliev's higher-spin gravity
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• An Action for Matter Coupled Higher Spin Gravity in Three Dimensions
• Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT
• A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS
• New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity
• Singletons and their maximal symmetry algebras
• Classical double copy and higher-spin fields
• Planar solutions of higher-spin theory I: free field level
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• The holographic dual of the Penrose transform
• Higher spin gauge theory on fuzzy $S_N^4$
• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• Higher spin fluctuations on spinless 4D BTZ black hole
• Higher-spin gauge theories in three spacetime dimensions
• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• Finite higher spin transformations from exponentiation
• 3d conformal fields with manifest $sl(2,\mathbb{C})$
• Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras
• Linearized Coxeter Higher-Spin Theories
• Simple Unfolded Equations for Massive Higher Spins in AdS${}_3$
• Towards Massless Sector of Tensionless Strings on $Ad{S}_5$
• On tensionless string field theory in AdS${}_3$
• Classical and quantum particles from nongeneric conformal orbits
• Higher spin interactions: cubic deformations on Minkowski and (Anti)de Sitter backgrounds
• Higher-spin initial data in twistor space with complex stargenvalues
• On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity