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.

160 pages, minor corrections

References in corpus (30)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Light-Front Higher-Spin Theories in Flat Space
• Higher Spins in AdS and Twistorial Holography
• AdS_4/CFT_3 Construction from Collective 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
• BRST approach to Lagrangian construction for fermionic higher spin fields in AdS space
• Frame-like gauge invariant formulation for massive high spin particles
• Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields
• Classical and quantum stability of higher-derivative dynamics
• Chiral Higher Spin Theories and Self-Duality
• Consistent couplings between spin-2 and spin-3 massless fields
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space
• Elementary particles with continuous spin
• Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra
• FV-type action for AdS(5) mixed-symmetry fields
• Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields
• Transverse Invariant Higher Spin Fields
• Higher-Spin Algebras, Holography and Flat Space
• On triviality of S-matrix in conformal higher spin theory
• Flato-Fronsdal theorem for higher-order singletons
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• Massive spin-2 in the Fradkin-Vasiliev formalism. I. Partially massless case
• Test of the local form of higher-spin equations via AdS/CFT
• A Riccati type PDE for light-front higher helicity vertices

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