Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices

Abstract

This work completes the classification of the cubic vertices for arbitrary spin massless bosons in three dimensions started in a previous companion paper by constructing parity-odd vertices. Similarly to the parity-even case, there is a unique parity-odd vertex for any given triple $s_1\ge s_2\ge s_3\ge 2$ of massless bosons if the triangle inequalities are satisfied ($s_1<s_2+s_3$) and none otherwise. These vertices involve two (three) derivatives for odd (even) values of the sum $s_1+s_2+s_3$. A non-trivial relation between parity-even and parity-odd vertices is found. Similarly to the parity-even case, the scalar and Maxwell matter can couple to higher spins through current couplings with higher derivatives. We comment on possible lessons for 2d CFT. We also derive both parity-even and parity-odd vertices with Chern-Simons fields and comment on the analogous classification in two dimensions.

arXiv comment29 pages

References in corpus (72)

• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Spinning Conformal Correlators
• An AdS_3 Dual for Minimal Model CFTs
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Cubic interaction vertices for massive and massless higher spin fields
• xTras: a field-theory inspired xAct package for Mathematica
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• String Lessons for Higher-Spin Interactions
• Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
• Light-Front Higher-Spin Theories in Flat Space
• Cubic interaction vertices for fermionic and bosonic arbitrary spin fields
• On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• General trilinear interaction for arbitrary even higher spin gauge fields
• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• Current Exchanges and Unconstrained Higher Spins
• A generating function for the cubic interactions of higher spin fields
• 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
• Higher-spin Interactions from CFT: The Complete Cubic Couplings
• Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions
• Higher-Spin Gauge Theories and Bulk Locality
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Towards metric-like higher-spin gauge theories in three dimensions
• On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background
• Chiral Higher Spin Theories and Self-Duality
• Consistent couplings between spin-2 and spin-3 massless fields
• Scalar fields and three-point functions in D=3 higher spin gravity
• On higher spin interactions with matter
• Maxwell-like Lagrangians for higher spins
• On spin 3 interacting with gravity
• Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space
• Spin 3 cubic vertices in a frame-like formalism
• Cubic interactions of Maxwell-like higher spins
• On four-point interactions in massless higher spin theory in flat space
• A Note on (Non)-Locality in Holographic Higher Spin Theories
• Exceptional F(4) Higher-Spin Theory in AdS(6) at One-Loop and other Tests of Duality
• Direct construction of a cubic selfinteraction for higher spin gauge fields
• Higher-Spin Algebras, Holography and Flat Space
• On the Non-Local Obstruction to Interacting Higher Spins in Flat Space
• Off-shell construction of some trilinear higher spin gauge field interactions
• Parity violating vertices for spin-3 gauge fields
• Notes on higher-spin algebras: minimal representations and structure constants
• On Killing tensors and cubic vertices in higher-spin gauge theories
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• Higher Spins and Matter Interacting in Dimension Three
• On the Local Frame in Nonlinear Higher-Spin Equations
• Conformal invariant interaction of a scalar field with the higher spin field in AdS_{D}
• Cubic interactions of massless bosonic fields in three dimensions
• Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space
• An Exotic Theory of Massless Spin-Two Fields in Three Dimensions
• On current contribution to Fronsdal equations
• Quantizing higher-spin gravity in free-field variables
• Rainbow Valley of Colored (Anti) de Sitter Gravity in Three Dimensions
• On higher spin extension of the Jackiw-Teitelboim gravity model
• Interacting Fields of Arbitrary Spin and N>4 Supersymmetric Self-dual Yang-Mills Equations
• Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space
• On big crunch solutions in Prokushkin-Vasiliev theory
• Low-spin models for higher-spin Lagrangians
• Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes
• Feynman rules for higher-spin gauge fields on AdS${}_{d+1}$
• Metric- and frame-like higher-spin gauge theories in three dimensions
• Iterating free-field AdS/CFT: higher spin partition function relations
• A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS
• Cubic-interaction-induced deformations of higher-spin symmetries
• Perturbative analysis in higher-spin theories
• Rainbow Vacua of Colored Higher Spin Gravity in Three Dimensions
• Action principles for higher and fractional spin gravities
• On generating functions of Higher Spin cubic interactions
• Novel generalization of three-dimensional Yang-Mills theory
• Higher Spin Black Holes in Three Dimensions: Comments on Asymptotics and Regularity
• Coupling coefficient in three dimensional higher spin holography

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• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• Cubic interactions for arbitrary spin N-extended massless supermultiplets in 4d flat space
• Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space
• Basic introduction to higher-spin theories
• Cubic interactions of massless bosonic fields in three dimensions
• Interacting massive and massless arbitrary spin fields in 4d flat space
• Looking for partially-massless gravity
• Vertex-Constraints in 3D Higher Spin Theories
• Cubic interactions of arbitrary spin fields in 3d flat space
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation
• Constraints for Three-Dimensional Higher-Spin Interactions and Conformal Correlators
• Cubic Interaction for Higher Spins in $Ad{S}_{d+1}$ space in the explicit covariant form
• On BF-type higher-spin actions in two dimensions
• Higher-spin gauge theories in three spacetime dimensions
• A note on higher-order vertices of higher-spin fields in flat and (A)dS space
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• Massless higher spin cubic vertices in flat four dimmensional space
• Superspace First Order Formalism, Trivial Symmetries and Electromagnetic Interactions of Linearized Supergravity
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Massless spin 2 interacting with massive higher spins in d=3
• AdS${}_3$/AdS${}_2$ degression of massless particles
• On higher spin cubic interactions in d=3
• AdS${}_3$/AdS${}_2$ degression of Fronsdal fields