Basic introduction to higher-spin theories

Abstract

This is a collection of my lecture notes on the higher-spin theory course given for students at the Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University. The goal of these lectures is to give an introduction to higher-spin theories accessible to master level students which would enable them to read the higher-spin literature. I start by introducing basic relevant notions of representation theory and the associated field-theoretic descriptions. Focusing on massless symmetric fields I review different approaches to interactions as well as the no-go results. I end the lectures by reviewing some of the currently available positive results on interactions of massless higher-spin fields, namely, holographic, Chern-Simons and chiral higher-spin theories.

arXiv comment160 pages, minor corrections

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• An AdS_3 Dual for Minimal Model CFTs
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• Local BRST cohomology in the antifield formalism: I. General theorems
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Cubic interaction vertices for massive and massless higher spin fields
• Minimal Model Holography
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• Inconsistency of interacting, multi-graviton theories
• On higher spins and the tensionless limit of String Theory
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Causality Constraints in Conformal Field Theory
• Introduction to the Classical Theory of Higher Spins
• String Lessons for Higher-Spin Interactions
• The Higher Spin/Vector Model Duality
• The self-dual sector of QCD amplitudes
• Free geometric equations for higher spins
• How massless are massless fields in $Ad{S}_d$
• Conformal Higher Spin Theory
• Light-Front Higher-Spin Theories in Flat Space
• On the geometry of higher-spin gauge fields
• Higher Spins in AdS and Twistorial Holography
• Cubic interaction vertices for fermionic and bosonic arbitrary spin fields
• Lagrangian formulation of the massless higher integer spin fields in the AdS background
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• Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory
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• Geometric Formulation for Partially Massless Fields
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• Current Exchanges and Unconstrained Higher Spins
• On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
• Cubic interactions of massless higher spins in (A)dS: metric-like approach
• Consistent deformations of dual formulations of linearized gravity: A no-go result
• Higher-spin Interactions from CFT: The Complete Cubic Couplings
• Higher Spin Superalgebras in any Dimension and their Representations
• Quantum Chiral Higher Spin Gravity
• Introduction to the Maldacena Conjecture on AdS/CFT
• Higher-Spin Gauge Theories and Bulk Locality
• On the Frame-Like Formulation of Mixed-Symmetry Massless Fields in (A)dS(d)
• Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions
• BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space
• Frame-like gauge invariant formulation for massive high spin particles
• Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields
• Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields
• Towards metric-like higher-spin gauge theories in three dimensions
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Classical and quantum stability of higher-derivative dynamics
• Light-Front Bootstrap for Chern-Simons Matter Theories
• Chiral Higher Spin Theories and Self-Duality
• Consistent couplings between spin-2 and spin-3 massless fields
• 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
• No Self-Interaction for Two-Column Massless Fields
• On higher spin interactions with matter
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• Maxwell-like Lagrangians for higher spins
• Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space
• Actions for Self-dual Higher Spin Gravities
• Light-cone gauge cubic interaction vertices for massless fields in AdS(4)
• Higher-spin current multiplets in operator-product expansions
• Elementary particles with continuous spin
• Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space
• Exploring the S-Matrix of Massless Particles
• Cubic interactions of Maxwell-like higher spins
• Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra
• On four-point interactions in massless higher spin theory in flat space
• FV-type action for AdS(5) mixed-symmetry fields
• Gravitational cubic interactions for a simple mixed-symmetry gauge field in AdS and flat backgrounds
• Fermionic fields in the d-dimensional anti-de Sitter spacetime
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions
• Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields
• Infinite (continuous) spin fields in the frame-like formalism
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Transverse Invariant Higher Spin Fields
• Higher-Spin Algebras, Holography and Flat Space
• On triviality of S-matrix in conformal higher spin theory
• On the Non-Local Obstruction to Interacting Higher Spins in Flat Space
• Parity violating vertices for spin-3 gauge fields
• Conformal higher spin scattering amplitudes from twistor space
• On quantum corrections in higher-spin theory in flat space
• Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
• Flato-Fronsdal theorem for higher-order singletons
• Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations
• Notes on higher-spin algebras: minimal representations and structure constants
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• On the quantum structure of space-time, gravity, and higher spin in matrix models
• Scalar scattering via conformal higher spin exchange
• Massive spin-2 in the Fradkin-Vasiliev formalism. I. Partially massless case
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• One-loop Test of Free SU(N) Adjoint Model Holography
• Arbitrary spin massless bosonic fields in d-dimensional anti-de Sitter space
• On the gauge symmetries of Maxwell-like higher-spin Lagrangians
• Test of the local form of higher-spin equations via AdS/CFT
• Bulk quartic vertices from boundary four-point correlators
• Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six Dimensions
• Pseudo-local Theories: A Functional Class Proposal
• Conformal Higher Spin Theory and Twistor Space Actions
• Spinor helicity structures in higher spin theories
• A Riccati type PDE for light-front higher helicity vertices
• Cubic-interaction-induced deformations of higher-spin symmetries
• The Conformal Characters
• Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras

Cited by in corpus (10)

• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• Higher-spin gauge theories in three spacetime dimensions
• BRST-BV approach for interacting higher spin fields
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
• Consistent Lagrangians for irreducible interacting higher-spin fields with holonomic constraints
• On the electromagnetic interaction and the anomalous term in the Duffin-Kemmer-Petiau theory
• Massless chiral fields in six dimensions
• Higher spin Lagrangians from higher derivative diffeomorphisms
• Topological Fields in $4d$ Higher Spin Theory