A Riccati type PDE for light-front higher helicity vertices

Abstract

This paper is based on a curious observation about an equation related to the tracelessness constraints of higher spin gauge fields. The equation also occurs in the theory of continuous spin representations of the Poincaré group. Expressed in an oscillator basis for the higher spin fields, the equation becomes a non-linear partial differential operator of the Riccati type acting on the vertex functions. The consequences of the equation for the cubic vertex is investigated in the light-front formulation of higher spin theory. The classical vertex is completely fixed but there is room for off-shell quantum corrections.

27 pages. Updated to published version

References in corpus (24)

• Closed String Field Theory: Quantum Action and the BV Master Equation
• Introduction to string field theory
• Introduction to sh Lie algebras for physicists
• Local BRST cohomology in gauge theories
• Self-Interaction and Gauge Invariance
• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Cubic interaction vertices for massive and massless higher spin fields
• How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples
• String Lessons for Higher-Spin Interactions
• Cubic interaction vertices for fermionic and bosonic arbitrary spin fields
• On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory
• General trilinear interaction for arbitrary even higher spin gauge fields
• 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
• Higher-Spin Interactions: four-point functions and beyond
• On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background
• Consistent couplings between spin-2 and spin-3 massless fields
• Higher Spin Gauge Theories in Any Dimension
• Consistent Interactions between Gauge Fields and Local BRST Cohomology : The Example of Yang-Mills Models
• BRST Theory for Continuous Spin
• Spinor helicity structures in higher spin theories
• Structure of Higher Spin Gauge Interactions
• An Abstract Interface to Higher Spin Gauge Field Theory
• Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity

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• Light-Front Higher-Spin Theories in Flat Space
• Chiral Higher Spin Theories and Self-Duality
• Actions for Self-dual Higher Spin Gravities
• Cubic interactions of Maxwell-like higher spins
• Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure
• Basic introduction to higher-spin theories
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$
• Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• Scalar Fields in 3D Asymptotically Flat Higher-Spin Gravity
• A Twistorial Description of the IKKT-Matrix Model
• 3d conformal fields with manifest $sl(2,\mathbb{C})$
• Fermi-Bose cubic couplings in light-cone field theories
• On-Shell Gauge Invariant Three-Point Amplitudes