Vertex-Constraints in 3D Higher Spin Theories

Abstract

We analyse the constraints imposed by gauge invariance on higher-order interactions between massless bosonic fields in three-dimensional higher-spin gravities. We show that vertices of quartic and higher order that are independent of the cubic ones can only involve scalars and Maxwell fields. As a consequence, the full non-linear interactions of massless higher-spin fields are completely fixed by the cubic vertex.

arXiv comment5 pages

References in corpus (35)

• AdS Dual of the Critical O(N) Vector Model
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• An AdS_3 Dual for Minimal Model CFTs
• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Cubic interaction vertices for massive and massless higher spin fields
• String Lessons for Higher-Spin Interactions
• The Higher Spin/Vector Model Duality
• Higher Spins & Strings
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• General trilinear interaction for arbitrary even higher spin gauge fields
• Higher spin theory in 3-dimensional flat space
• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• 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: four-point functions and beyond
• Higher-Spin Gauge Theories and Bulk Locality
• Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions
• BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields
• Towards metric-like higher-spin gauge theories in three dimensions
• String Theory as a Higher Spin Theory
• Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space
• 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
• Direct construction of a cubic selfinteraction for higher spin gauge fields
• On the Non-Local Obstruction to Interacting Higher Spins in Flat Space
• Gravitational Interactions of Higher-Spin Fermions
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• Cubic interactions of massless bosonic fields in three dimensions
• Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space
• Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes
• Metric- and frame-like higher-spin gauge theories in three dimensions
• On generating functions of Higher Spin cubic interactions

Cited by in corpus (13)

• 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
• 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
• Restrictions for $n$-Point Vertices in Higher-Spin Theories
• Cubic Interaction for Higher Spins in $Ad{S}_{d+1}$ space in the explicit covariant form
• Higher-spin gauge theories in three spacetime dimensions
• A note on higher-order vertices of higher-spin fields in flat and (A)dS space
• Colourful Poincaré symmetry, gravity and particle actions
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$