Elements of Vasiliev theory

Abstract

We propose a self-contained description of Vasiliev higher-spin theories with the emphasis on nonlinear equations. The main sections are supplemented with some additional material, including introduction to gravity as a gauge theory; the review of the Fronsdal formulation of free higher-spin fields; Young diagrams and tensors as well as sections with advanced topics. The shortest route to Vasiliev equations covers 40 pages. The general discussion is dimension independent, while the essence of the Vasiliev formulation is discussed on the base of the four-dimensional higher-spin theory. Three-dimensional and $d$-dimensional higher-spin theories follow the same logic.

further typos corrected; four figures; 161 pages

References in corpus (14)

• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Current Exchanges and Unconstrained Higher Spins
• A generating function for the cubic interactions of higher spin fields
• BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space
• BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields
• Consistent couplings between spin-2 and spin-3 massless fields
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra
• FV-type action for AdS(5) mixed-symmetry fields
• Transverse Invariant Higher Spin Fields
• Higher Spins and String Interactions
• Generalised connections and higher-spin equations
• Gauge Symmetry and Consistent Spin-Two Theories

Cited by in corpus (74)

• Bounding the Space of Holographic CFTs with Chaos
• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Cubic interactions of Maxwell-like higher spins
• Higher-Spin Theory and Space-Time Metamorphoses
• BRST approach to Lagrangian construction for bosonic continuous spin field
• From Higher Spins to Strings: A Primer
• TASI Lectures on the Higher Spin - CFT duality
• Gauge Theory Formulations for Continuous and Higher Spin Fields
• Arbitrary spin conformal fields in (A)dS
• Higher Spin Dark Matter
• Chern-Simons Matter Theories and Higher Spin Gravity
• Formal Higher Spin Gravities
• Higher Spins and Matter Interacting in Dimension Three
• Massive higher spin fields in the frame-like multispinor formalism
• New Unfolded Higher Spin Systems in $Ad{S}_3$
• Cubic interactions of massless bosonic fields in three dimensions
• Lifshitz Holography with Isotropic Scale Invariance
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory
• General Cubic Interacting Vertex for Massless Integer Higher Spin Fields
• Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in AdS_3 space
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• FRW and domain walls in higher spin gravity
• Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?
• Massive higher spin supermultiplets unfolded
• On big crunch solutions in Prokushkin-Vasiliev theory
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• Higher spin de Sitter quasinormal modes
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Critical scaling in the large-$N$ $O(N)$ model in higher dimensions and its possible connection to quantum gravity
• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• A local action for fermionic unconstrained higher spin gauge fields in (A)dS space
• On unfolded off-shell formulation for higher-spin theory
• A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS
• Helicity decoupling in the massless limit of massive tensor fields
• Higher Spin Gravities and Presymplectic AKSZ Models
• Higher Spin Lifshitz Theories and the KdV-Hierarchy
• Symmetries of higher-spin current interactions in four dimensions
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Constraints for Three-Dimensional Higher-Spin Interactions and Conformal Correlators
• Planar solutions of higher-spin theory I: free field level
• Cubic Interaction for Higher Spins in $Ad{S}_{d+1}$ space in the explicit covariant form
• Higher Spin Lifshitz Theory and Integrable Systems
• Higher spin gauge theory on fuzzy $S_N^4$
• Hochschild cohomology of the Weyl algebra and Vasiliev's equations
• Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background
• Supersymmetric electric-magnetic duality of hypergravity
• Homotopy Algebras in Higher Spin Theory
• A Note on Circle Compactification of Tensile Ambitwistor String
• Conformal symmetry for relativistic point particles
• Aspects of Higher-Spin Theory with Fermions
• A note on higher spin symmetry in the IIB matrix model with the operator interpretation
• Hypergravity in five dimensions
• Fermionic higher-spin triplets in AdS
• Quasiconformal Group Approach to Higher Spin Algebras, their Deformations and Supersymmetric Extensions
• Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange
• Gauging the higher-spin-like symmetries by the Moyal product
• CMB B-modes, spinorial space-time and Pre-Big Bang (II)
• Topics in Asymptotic Symmetries and Infrared Effects
• Lagrangian formulation of the massive higher spin supermultiplets in three dimensional space-time
• Coupling coefficient in three dimensional higher spin holography
• Two-twistor particle models and free massive higher spin fields
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter
• Symmetries and Invariants in Higher-Spin Theory
• Tensor Field Theories: Renormalization and Random Geometry
• On Gluing CFT Correlators to Higher-Spin Amplitudes in AdS
• Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• Non-Lagrangian Gauge Field Models are Physically Excluded
• On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity
• Interactions in MacDowell-Mansouri Gravitation
• Theories of Massive Gravity in 2+1 Dimensions