Nonlinear higher spin theories in various dimensions

Abstract

In this article, an introduction to the nonlinear equations for completely symmetric bosonic higher spin gauge fields in anti de Sitter space of any dimension is provided. To make the presentation self-contained we explain in detail some related issues such as the MacDowell-Mansouri-Stelle-West formulation of gravity, unfolded formulation of dynamical systems in terms of free differential algebras and Young tableaux symmetry properties in terms of Howe dual algebras.

85 pages, Latex; v2: added references, corrected typos; v3: minor corrections: coefficients in two equations and typos corrected, acknowledgements added

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Cited by in corpus (261)

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• Static BPS black hole in 4d higher-spin gauge theory
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• Cubic interactions of massless higher spins in (A)dS: metric-like approach
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Higher-Spin Interactions: four-point functions and beyond
• Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimentions
• Higher-Spin Gauge Theories and Bulk Locality
• BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space
• Universal Limits on Massless High-Spin Particles
• Frame-like gauge invariant formulation for massive high spin particles
• Tensor gauge fields in arbitrary representations of GL(D,R): II. Quadratic actions
• Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields
• Towards metric-like higher-spin gauge theories in three dimensions
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields
• Elements of Vasiliev theory
• Bosonic conformal higher--spin fields of any symmetry
• Minimal Local Lagrangians for Higher-Spin Geometry
• On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
• Biaxially symmetric solutions to 4D higher-spin gravity
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• Describing Curved Spaces by Matrices
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• Families of exact solutions to Vasiliev's 4D equations with spherical, cylindrical and biaxial symmetry
• Unified BRST description of AdS gauge fields
• Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime
• On higher spin interactions with matter
• Generating functions of (partially-)massless higher-spin cubic interactions
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• Supersymmetric Chern-Simons Theories with Vector Matter
• Brane Partons and Singleton Strings
• Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex
• On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space
• Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type
• Mixed-Symmetry Massless Fields in Minkowski space Unfolded
• Higher spin black hole entropy in three dimensions
• Massless Poincare modules and gauge invariant equations
• Correlation Functions in Holographic Minimal Models
• Massive Higher Derivative Gravity in D-dimensional Anti-de Sitter Spacetimes
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• Spin 3 cubic vertices in a frame-like formalism
• Tractors, Mass and Weyl Invariance
• Cubic interactions of Maxwell-like higher spins
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• String Theory and The Velo-Zwanziger Problem
• FV-type action for AdS(5) mixed-symmetry fields
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• Gauge fields in (A)dS within the unfolded approach: algebraic aspects
• Parent form for higher spin fields on anti-de Sitter space
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• (A)dS exchanges and partially-massless higher spins
• Shift Symmetries in (Anti) de Sitter Space
• More on La Grande Bouffe: towards higher spin symmetry breaking in AdS
• Partially-massless higher-spin algebras and their finite-dimensional truncations
• Non-Abelian tensor gauge fields: generalization of Yang-Mills theory
• Direct construction of a cubic selfinteraction for higher spin gauge fields
• Geometry and Observables in Vasiliev's Higher Spin Gravity
• String theory triplets and higher-spin curvatures
• Transverse Invariant Higher Spin Fields
• Reducible higher-spin multiplets in flat and AdS spaces and their geometric frame-like formulation
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields
• Bosons, fermions and anyons in the plane, and supersymmetry
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• BRST approach to Lagrangian construction for bosonic continuous spin field
• Weyl Invariance and the Origins of Mass
• Massive Higher Spins from BRST and Tractors
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• Gravitational Duality Transformations on (A)dS4
• Continuous spin fields of mixed-symmetry type
• TASI Lectures on the Higher Spin - CFT duality
• From Higher Spins to Strings: A Primer
• Spin-3 Topological Massive Gravity
• Off-shell construction of some trilinear higher spin gauge field interactions
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• Partition Functions for Higher-Spin theories in AdS
• Gravitational and higher-derivative interactions of massive spin 5/2 field in (A)dS space
• Comments on higher-spin holography
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. 2. Fermionic fields
• A note on higher-derivative actions for free higher-spin fields
• Cubic interaction vertex of higher-spin fields with external electromagnetic field
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• The Holographic Geometry of the Renormalization Group and Higher Spin Symmetries
• Towards higher-spin holography in ambient space of any dimension
• Conformal Field Theory and Algebraic Structure of Gauge Theory
• Unfolded Description of $Ad{S}_4$ Kerr Black Hole
• Detours and Paths: BRST Complexes and Worldline Formalism
• Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spaces
• Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS_3 space
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• Higher-spin Chern-Simons theories in odd dimensions
• The Exact Renormalization Group and Higher-spin Holography
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• On the Algebraic Structure of Higher-Spin Field Equations and New Exact Solutions
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• Gauge invariants and Killing tensors in higher-spin gauge theories
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• CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge
• Higher Spins and Matter Interacting in Dimension Three
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• Higher Spin Scattering in Superstring Theory
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$
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• Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS_d space
• Lifshitz Holography with Isotropic Scale Invariance
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• 1/N and Loop Corrections in Higher Spin AdS_4/CFT_3 Duality
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• General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory
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• Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in AdS_3 space
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• Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
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• Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?
• Matrix Theory for Baryons: An Overview of Holographic QCD for Nuclear Physics
• Dual descriptions of spin two massive particles in $D=2+1$ via master actions
• A Higgs Mechanism for Gravity. Part II: Higher Spin Connections
• Low-spin models for higher-spin Lagrangians
• A Compendium of Sphere Path Integrals
• Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes
• The Generalized Curvature and Christoffel Symbols for a Higher Spin Potential in AdS_{d+1} Space
• SFT-inspired Algebraic Structures in Gauge Theories
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• A dual lagrangian for non-Abelian tensor gauge fields
• On Higher Spin Symmetries in AdS_{5}
• Manifest Form of the Spin-Local Higher-Spin Vertex ${{\rm Y}}_{\omega CCC}^{\eta \eta }$
• Higher Spins from Nonlinear Realizations of $OSp(1|8)$
• Old and New No Go Theorems on Interacting Massless Particles in Flat Space
• BRST approach to higher spin field theories
• Characteristic Cohomology and Observables in Higher Spin Gravity
• On Dimensional Degression in AdS(d)
• On Nonlinear Higher Spin Curvature
• Brief review on higher spin black holes
• Precision Spectroscopy and Higher Spin symmetry in the ABJM model
• Galilean contractions of $W$-algebras
• Solutions of Free Higher Spins in AdS
• A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS
• Higher Spin Holography, RG, and the Light Cone
• The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
• An action for higher spin gauge theory in four dimensions
• Geometry and dynamics of higher-spin frame fields
• Higher Spin Gravities and Presymplectic AKSZ Models
• Master Higher-Spin Particle
• An infinite supermultiplet of massive higher-spin fields
• Singletons and their maximal symmetry algebras
• Higher Spin Lifshitz Theories and the KdV-Hierarchy
• Symmetries of higher-spin current interactions in four dimensions
• Unfolding versus BRST and currents in Sp(2M) invariant higher-spin theory
• Planar solutions of higher-spin theory I: free field level
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Low Tension Strings on a Cosmological Singularity
• Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields
• On manifolds admitting the consistent Lagrangian formulation for higher spin fields
• Holographic Chern-Simons Theories
• Unfolded Dynamics and Parameter Flow of Generic AdS(4) Black Hole
• Higher Spin Lifshitz Theory and Integrable Systems
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• Towards Unifying Structures in Higher Spin Gauge Symmetry
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• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
• BRST Lagrangian construction for spin-2 field in Einstein space
• Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model
• Higher Spin Theory - Part I
• Bosonic Massless Higher Spin Fields from Matrix Model
• Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background
• Higher-spin gauge theories in three spacetime dimensions
• Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields
• Unfolded Equations for Current Interactions of 4d Massless Fields as a Free System in Mixed Dimensions
• Quantum Correction of the Wilson Line and Entanglement Entropy in the Pure AdS${}_3$ Einstein Gravity Theory
• Propagating modes of non-Abelian tensor gauge field of second rank
• Finite higher spin transformations from exponentiation
• On the fermionic Grande Bouffe: more on higher spin symmetry breaking in AdS/CFT
• Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory
• Scattering of charged tensor bosons in gauge and superstring theories
• On manifestly sp(2) invariant formulation of quadratic higher spin Lagrangians
• Holographic Renormalisation for the Spin-3 Theory and the (A)dS3/CFT2 correspondence
• Strings on AdS_2 and the High-Energy Limit of Noncritical M-Theory
• Gauge dependence of vacuum expectation values of gauge invariant operators from soft breaking of BRST symmetry. Example of Gribov-Zwanziger action
• BRST-BV approach for interacting higher spin fields
• Fermionic higher-spin triplets in AdS
• On Lagrangian formulations for mixed-symmetry HS fields on AdS spaces within BFV-BRST approach
• Star-Product Functions in Higher-Spin Theory and Locality
• Interpolating between $a$ and $F$
• Gauge invariant Lagrangian for non-Abelian tensor gauge fields of fourth rank
• BPS preons and the AdS-M-algebra
• Non-Minimal Higher-Spin DS4/CFT3
• Higher Spins and Current Exchanges
• Towards the structure of a cubic interaction vertex for massless integer higher spin fields
• One loop partition function of six dimensional conformal gravity using heat kernel on AdS
• Quasiconformal Group Approach to Higher Spin Algebras, their Deformations and Supersymmetric Extensions
• Non-Abelian Tensor Gauge Fields. Enhanced Symmetries
• Gauging the higher-spin-like symmetries by the Moyal product
• Unconstrained $\mathcal{N}=2$ higher-spin gauge superfields and their hypermultiplet couplings
• 4D Localization in Randall-Sundrum 2 Supergravity and in Vasiliev Theories
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• Topics in Asymptotic Symmetries and Infrared Effects
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• Higher Spin Particles with Bosonic Counterpart of Supersymmetry
• Strings vs Spins on the Null Orbifold
• On the variational principle in the unfolded dynamics
• Interaction of Non-Abelian Tensor Gauge Fields
• Massive Kaluza-Klein Theories and their Spontaneously Broken Symmetries
• Non-Abelian tensor gauge fields and extended current algebra. Generalization of Yang-Mills theory
• On Lagrangian Formulation for Spin (2,1,1) Massive Tensor Field on Minkowski Backgrounds
• Lagrangian formulation of the massive higher spin supermultiplets in three dimensional space-time
• Massless chiral fields in six dimensions
• Unfolding $E_{11}$
• Higher Spin Fields and Symplectic Geometry
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter
• Unit Invariance as a Unifying Principle of Physics
• Higher spin fields with reversed spin-statistics relation
• Massless infinite spin (super)particles and fields
• Conserved Higher-Spin Charges in $Ad{S}_4$
• Tensor Field Theories: Renormalization and Random Geometry
• Programming Realization of Symbolic Computations for Non-linear Commutator Superalgebras over the Heisenberg--Weyl Superalgebra: Data Structures and Processing Methods
• Supersymmetric higher spin models in three dimensional spaces
• Bosonic Fradkin-Tseytlin equations unfolded. Irreducible case
• Bosonic Fradkin-Tseytlin equations unfolded
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• Group manifold approach to higher spin theory
• Higher spin interactions: cubic deformations on Minkowski and (Anti)de Sitter backgrounds
• BRST Extension of the Non-Linear Unfolded Formalism
• A model for massless higher spin field interacting with a geometrical background
• On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity
• Higher Spin Theories from Finsler Geometry
• Equation for one-loop divergences in two dimensions and its application to higher spin fields
• Bosonic Higher Spin Gravity in any Dimension with Dynamical Two-Form