Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes

Abstract

The dynamical commutators of the light-front Poincaré algebra yield first order differential equations in the $p^{+}$ momenta for the interaction vertex operators. The homogeneous solution to the equation for the quartic vertex is studied. Consequences as regards the constructibility assumption of quartic higher spin amplitudes from cubic amplitudes are discussed. The existence of quartic contact interactions unrelated to cubic interactions by Poincaré symmetry indicates that the higher spin S-matrix is not constructible. Thus quartic amplitude based no-go results derived by BCFW recursion for Minkowski higher spin massless fields may be circumvented.

28 pages. Small change of title (one instance of the word "quartic" removed) Minor corrections. Typos corrected. References added

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• Conformal higher spin scattering amplitudes from twistor space
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• Vertex-Constraints in 3D Higher Spin Theories
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation
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• Cubic Interaction for Higher Spins in $Ad{S}_{d+1}$ space in the explicit covariant form
• A note on higher-order vertices of higher-spin fields in flat and (A)dS space
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• Deriving spin-1 quartic interaction vertices from closure of the Poincaré algebra
• General light-cone gauge approach to conformal fields and applications to scalar and vector fields
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins