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 (258)

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• Current Exchanges and Unconstrained Higher Spins
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• Static BPS black hole in 4d higher-spin gauge theory
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• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
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• BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space
• Universal Limits on Massless High-Spin Particles
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• 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
• Unconstrained Higher Spins of Mixed Symmetry. I. Bose Fields
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• 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
• An Exact Solution of 4D Higher-Spin Gauge Theory
• Biaxially symmetric solutions to 4D higher-spin gravity
• Describing Curved Spaces by Matrices
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• 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
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• Brane Partons and Singleton Strings
• On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields
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• Mixed-Symmetry Massless Fields in Minkowski space Unfolded
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• Spin 3 cubic vertices in a frame-like formalism
• Tractors, Mass and Weyl Invariance
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• String Theory and The Velo-Zwanziger Problem
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• FV-type action for AdS(5) mixed-symmetry fields
• Parent form for higher spin fields on anti-de Sitter space
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• Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions
• (A)dS exchanges and partially-massless higher spins
• Shift Symmetries in (Anti) de Sitter Space
• Partially-massless higher-spin algebras and their finite-dimensional truncations
• More on La Grande Bouffe: towards higher spin symmetry breaking in AdS
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• Direct construction of a cubic selfinteraction for higher spin gauge fields
• Non-Abelian tensor gauge fields: generalization of Yang-Mills theory
• Transverse Invariant Higher Spin Fields
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• Aspects of Three-dimensional Spin-4 Gravity
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields
• Bosons, fermions and anyons in the plane, and supersymmetry
• BRST approach to Lagrangian construction for bosonic continuous spin field
• Weyl Invariance and the Origins of Mass
• Continuous spin fields of mixed-symmetry type
• Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons
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• TASI Lectures on the Higher Spin - CFT duality
• Spin-3 Topological Massive Gravity
• Off-shell construction of some trilinear higher spin gauge field interactions
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• Partition Functions for Higher-Spin theories in AdS
• Comments on higher-spin holography
• Gravitational and higher-derivative interactions of massive spin 5/2 field in (A)dS space
• 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
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• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• Cubic interaction vertex of higher-spin fields with external electromagnetic field
• 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
• The Exact Renormalization Group and Higher-spin Holography
• Effective action for higher spin fields on (A)dS backgrounds
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• Frame-like gauge invariant formulation for mixed symmetry fermionic fields
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• Lifshitz Holography with Isotropic Scale Invariance
• Off-shell Gauge Fields from BRST Quantization
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• General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory
• U(N) spinning particles and higher spin equations on complex manifolds
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• Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
• Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?
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• 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
• Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes
• A Compendium of Sphere Path Integrals
• The Generalized Curvature and Christoffel Symbols for a Higher Spin Potential in AdS_{d+1} Space
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• SFT-inspired Algebraic Structures in Gauge Theories
• A dual lagrangian for non-Abelian tensor gauge fields
• On Higher Spin Symmetries in AdS_{5}
• Old and New No Go Theorems on Interacting Massless Particles in Flat Space
• Higher Spins from Nonlinear Realizations of $OSp(1|8)$
• Manifest Form of the Spin-Local Higher-Spin Vertex ${{\rm Y}}_{\omega CCC}^{\eta \eta }$
• BRST approach to higher spin field theories
• On Dimensional Degression in AdS(d)
• On Nonlinear Higher Spin Curvature
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Galilean contractions of $W$-algebras
• Brief review on higher spin black holes
• Precision Spectroscopy and Higher Spin symmetry in the ABJM model
• An action for higher spin gauge theory in four dimensions
• Higher Spin Holography, RG, and the Light Cone
• The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
• 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
• Geometry and dynamics of higher-spin frame fields
• An infinite supermultiplet of massive higher-spin fields
• Master Higher-Spin Particle
• Singletons and their maximal symmetry algebras
• Higher Spin Gravities and Presymplectic AKSZ Models
• Symmetries of higher-spin current interactions in four dimensions
• Schwinger-Fronsdal Theory of Abelian Tensor Gauge Fields
• Unfolding versus BRST and currents in Sp(2M) invariant higher-spin theory
• Low Tension Strings on a Cosmological Singularity
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Planar solutions of higher-spin theory I: free field level
• Higher Spin Lifshitz Theories and the KdV-Hierarchy
• Higher Spin Lifshitz Theory and Integrable Systems
• Holographic Chern-Simons Theories
• On manifolds admitting the consistent Lagrangian formulation for higher spin fields
• Unfolded Dynamics and Parameter Flow of Generic AdS(4) Black Hole
• Towards Unifying Structures in Higher Spin Gauge Symmetry
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• Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model
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• Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians
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• 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
• Higher Spin Theory - Part I
• Bosonic Massless Higher Spin Fields from Matrix Model
• Propagating modes of non-Abelian tensor gauge field of second rank
• 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
• Finite higher spin transformations from exponentiation
• Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory
• On the fermionic Grande Bouffe: more on higher spin symmetry breaking in AdS/CFT
• Scattering of charged tensor bosons in gauge and superstring theories
• Strings on AdS_2 and the High-Energy Limit of Noncritical M-Theory
• On manifestly sp(2) invariant formulation of quadratic higher spin Lagrangians
• Gauge dependence of vacuum expectation values of gauge invariant operators from soft breaking of BRST symmetry. Example of Gribov-Zwanziger action
• Holographic Renormalisation for the Spin-3 Theory and the (A)dS3/CFT2 correspondence
• On Lagrangian formulations for mixed-symmetry HS fields on AdS spaces within BFV-BRST approach
• Fermionic higher-spin triplets in AdS
• BRST-BV approach for interacting higher spin fields
• Gauge invariant Lagrangian for non-Abelian tensor gauge fields of fourth rank
• Star-Product Functions in Higher-Spin Theory and Locality
• Interpolating between $a$ and $F$
• BPS preons and the AdS-M-algebra
• One loop partition function of six dimensional conformal gravity using heat kernel on AdS
• Non-Minimal Higher-Spin DS4/CFT3
• Towards the structure of a cubic interaction vertex for massless integer higher spin fields
• Higher Spins and Current Exchanges
• Unconstrained $\mathcal{N}=2$ higher-spin gauge superfields and their hypermultiplet couplings
• Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange
• Non-Abelian Tensor Gauge Fields. Enhanced Symmetries
• 4D Localization in Randall-Sundrum 2 Supergravity and in Vasiliev Theories
• Gauging the higher-spin-like symmetries by the Moyal product
• Quasiconformal Group Approach to Higher Spin Algebras, their Deformations and Supersymmetric Extensions
• Interaction of Non-Abelian Tensor Gauge Fields
• Strings vs Spins on the Null Orbifold
• Topics in Asymptotic Symmetries and Infrared Effects
• Toward a Higher-Spin Dual of Interacting Field Theories
• On the variational principle in the unfolded dynamics
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• D2 Chern-Simons Gravity
• Higher Spin Particles with Bosonic Counterpart of Supersymmetry
• Unravelling Holographic Entanglement Entropy in Higher Spin Theories
• Unfolding $E_{11}$
• Non-Abelian tensor gauge fields and extended current algebra. Generalization of Yang-Mills theory
• Massless chiral fields in six dimensions
• Lagrangian formulation of the massive higher spin supermultiplets in three dimensional space-time
• On Lagrangian Formulation for Spin (2,1,1) Massive Tensor Field on Minkowski Backgrounds
• Higher spin fields with reversed spin-statistics relation
• Conserved Higher-Spin Charges in $Ad{S}_4$
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter
• Tensor Field Theories: Renormalization and Random Geometry
• Massless infinite spin (super)particles and fields
• Supersymmetric higher spin models in three dimensional spaces
• Higher Spin Fields and Symplectic Geometry
• Unit Invariance as a Unifying Principle of Physics
• Programming Realization of Symbolic Computations for Non-linear Commutator Superalgebras over the Heisenberg--Weyl Superalgebra: Data Structures and Processing Methods
• Higher spin interactions: cubic deformations on Minkowski and (Anti)de Sitter backgrounds
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• Bosonic Fradkin-Tseytlin equations unfolded
• Bosonic Fradkin-Tseytlin equations unfolded. Irreducible case
• Group manifold approach to higher spin theory
• Equation for one-loop divergences in two dimensions and its application to higher spin fields
• Higher Spin Theories from Finsler Geometry
• A model for massless higher spin field interacting with a geometrical background
• Bosonic Higher Spin Gravity in any Dimension with Dynamical Two-Form
• BRST Extension of the Non-Linear Unfolded Formalism
• On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity