On-Shell Gauge Invariant Three-Point Amplitudes

Abstract

Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices. Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches. Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions. Our analysis also shows that there exists a mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions, between a scalar field $\varphi$ and an antisymmetric rank-2 tensor field $A_{\mu \nu }$. Despite the well-known fact that in 4 dimensions rank-2 anti-symmetric fields are dual to scalar fields in free theories, such duality does not extend to interacting theories.

arXiv commentsignificantly revised, final version published in JHEP

References in corpus (11)

• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• Cubic interaction vertices for massive and massless higher spin fields
• String Lessons for Higher-Spin Interactions
• Light-Front Higher-Spin Theories in Flat Space
• General trilinear interaction for arbitrary even higher spin gauge fields
• Cubic interactions of massless higher spins in (A)dS: metric-like approach
• On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
• Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions
• Higher-Spin Algebras, Holography and Flat Space
• Graviton and gluon scattering from first principles
• A Riccati type PDE for light-front higher helicity vertices