Cubic interactions of massless bosonic fields in three dimensions

Abstract

Parity-even cubic vertices of massless bosons of arbitrary spins in three dimensional Minkowski space are classified in the metric-like formulation. As opposed to higher dimensions, there is at most one vertex for any given triple $s_1,s_2,s_3$ in three dimensions. All the vertices with more than three derivatives are of the type $(s,0,0)$, $(s,1,1)$ and $(s,1,0)$ involving scalar and/or Maxwell fields. All other vertices contain two (three) derivatives, when the sum of the spins is even (odd). Minimal coupling to gravity, $(s,s,2)$, has two derivatives and is universal for all spins (equivalence principle holds). Minimal coupling to Maxwell field, $(s,s,1)$, distinguishes spins $s\le 1$ and $s\ge 2$ as it involves one derivative in the former case and three derivatives in the latter case. Some consequences of this classification are discussed.

18 pages

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• 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
• Restrictions for $n$-Point Vertices in Higher-Spin Theories
• Higher-spin gauge theories in three spacetime dimensions
• The Uniqueness of Hypergravity
• 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
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• Superspace First Order Formalism, Trivial Symmetries and Electromagnetic Interactions of Linearized Supergravity
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• AdS${}_3$/AdS${}_2$ degression of massless particles
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• AdS${}_3$/AdS${}_2$ degression of Fronsdal fields