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

References in corpus (7)

• Consistency Conditions on the S-Matrix of Massless Particles
• On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
• On-shell constructibility of tree amplitudes in general field theories
• On triviality of S-matrix in conformal higher spin theory
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• The quintic interaction vertex in light-cone gravity
• Towards Unifying Structures in Higher Spin Gauge Symmetry

Cited by in corpus (2)

• Higher-Spin Algebras, Holography and Flat Space
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure