Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal

Abstract

We consider four-dimensional Higher-Spin Theory at the first nontrivial order corresponding to the cubic action. All Higher-Spin interaction vertices are explicitly obtained from Vasiliev's equations. In particular, we obtain the vertices that are not determined solely by the Higher-Spin algebra structure constants. The dictionary between the Fronsdal fields and Higher-Spin connections is found and the corrections to the Fronsdal equations are derived. These corrections turn out to involve derivatives of arbitrary order. We observe that the vertices not determined by the Higher-Spin algebra produce naked infinities, when decomposed into the minimal derivative vertices and improvements. Therefore, standard methods can only be used to check a rather limited number of correlation functions within the HS AdS/CFT duality. A possible resolution of the puzzle is discussed.

arXiv comment56 pages=40+Appendices; 1 figure; typos fixed, one ref added

References in corpus (41)

• AdS Dual of the Critical O(N) Vector Model
• Massless Higher Spins and Holography
• An AdS_3 Dual for Minimal Model CFTs
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Higher Spin Gauge Theories: Star-Product and AdS Space
• Nonlinear higher spin theories in various dimensions
• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• 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
• Constraining conformal field theories with a slightly broken higher spin symmetry
• The Higher Spin/Vector Model Duality
• Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
• Higher Spins in AdS and Twistorial Holography
• One Loop Tests of Higher Spin AdS/CFT
• On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory
• Higher-Spin Interactions: four-point functions and beyond
• On partition function and Weyl anomaly of conformal higher spin fields
• Elements of Vasiliev theory
• Analysis of Higher Spin Field Equations in Four Dimensions
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• Brane Partons and Singleton Strings
• Higher Spin Gravity Amplitudes From Zero-form Charges
• Geometry and Observables in Vasiliev's Higher Spin Gravity
• Higher Spin Conformal Currents in Minkowski Space
• Scalar Field in Any Dimension from the Higher Spin Gauge Theory Perspective
• Supersymmetric Higher Spin Theories
• Higher Spins and Matter Interacting in Dimension Three
• Uniformizing higher-spin equations
• Notes on conformal invariance of gauge fields
• 2D sigma models and differential Poisson algebras
• Vectorial AdS_5/CFT_4 duality for spin-one boundary theory
• Invariant Functionals in Higher-Spin Theory
• Unfolded Equations for Current Interactions of 4d Massless Fields as a Free System in Mixed Dimensions
• Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange

Cited by in corpus (65)

• Light-Front Bootstrap for Chern-Simons Matter Theories
• Actions for Self-dual Higher Spin Gravities
• A Derivation of AdS/CFT for Vector Models
• Veneziano Amplitude of Vasiliev Theory
• On the Non-Local Obstruction to Interacting Higher Spins in Flat Space
• From Higher Spins to Strings: A Primer
• TASI Lectures on the Higher Spin - CFT duality
• On quantum corrections in higher-spin theory in flat space
• Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations
• Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality
• Chern-Simons Matter Theories and Higher Spin Gravity
• Homotopy Operators and Locality Theorems in Higher-Spin Equations
• Basic introduction to higher-spin theories
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• On the Local Frame in Nonlinear Higher-Spin Equations
• Formal Higher Spin Gravities
• Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations
• One-loop Test of Free SU(N) Adjoint Model Holography
• Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes
• Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations
• Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• More on Chiral Higher Spin Gravity and Convex Geometry
• Bulk quartic vertices from boundary four-point correlators
• Toward a twistor action for chiral higher-spin gravity
• On current contribution to Fronsdal equations
• Minimal models of field theories: Chiral Higher Spin Gravity
• A Compendium of Sphere Path Integrals
• Minimal model of Chiral Higher Spin Gravity
• Chiral Higher Spin Gravity and Convex Geometry
• On one loop corrections in higher spin gravity
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• Noncommutative Wilson lines in higher-spin theory and correlation functions of conserved currents for free conformal fields
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Characteristic Cohomology and Observables in Higher Spin Gravity
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions
• ABJ Quadrality
• A Twistorial Description of the IKKT-Matrix Model
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Symmetries of higher-spin current interactions in four dimensions
• Bilinear Fronsdal currents in the $Ad{S}_4$ higher-spin theory
• Higher spin fluctuations on spinless 4D BTZ black hole
• Minimal models of field theories: SDYM and SDGR
• Ambitwistors, oscillators and massless fields on $Ad{S}_5$
• Higher-spin gauge theories in three spacetime dimensions
• Frame- and Metric-like Higher-Spin Fermions
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Constraining higher-spin S-matrices
• 3d conformal fields with manifest $sl(2,\mathbb{C})$
• Higher-spin gravity's "string": new gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution
• Explicit holography for vector models at finite $N$, volume and temperature
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Lorentz covariant form of extended higher-spin equations
• BRST-BV approach to massless fields adapted to AdS/CFT correspondence
• New diagrammatic framework for higher-spin gravity
• On correlation functions as higher-spin invariants
• Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in Arbitrary Higher-Spin Background
• A new higher-spin theory of supergravity in 2+1 dimensions
• On presymplectic structures for massless higher-spin fields
• Bosonic Higher Spin Gravity in any Dimension with Dynamical Two-Form
• On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity
• Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories