Off-Shell Spinor-Helicity Amplitudes from Light-Cone Deformation Procedure

TL;DR

This paper demonstrates that light-cone consistency conditions for massless fields in four dimensions can be reformulated as Ward identities for off-shell amplitudes, revealing a connection to the spinor-helicity formalism and aiding higher-spin interaction searches.

Contribution

It establishes a link between light-cone deformation procedures and off-shell spinor-helicity amplitudes, providing a general solution to the Ward identities for massless fields.

Findings

Off-shell light-cone amplitudes can be expressed as arbitrary functions of spinor products.

The light-cone consistent deformation procedure leads to an off-shell version of the spinor-helicity approach.

The approach facilitates the search for consistent interactions of massless higher-spin fields.

Abstract

We study the consistency conditions for interactions of massless fields of any spin in four-dimensional flat space using the light-cone approach. We show that they can be equivalently rewritten as the Ward identities for the off-shell light-cone amplitudes built from the light-cone Hamiltonian in the standard way. Then we find a general solution of these Ward identities. The solution admits a compact representation when written in the spinor-helicity form and is given by an arbitrary function of spinor products, satisfying well-known homogeneity constraints. Thus, we show that the light-cone consistent deformation procedure inevitably leads to a certain off-shell version of the spinor-helicity approach. We discuss how the relation between the two approaches can be employed to facilitate the search of consistent interaction of massless higher-spin fields.