Scattering Equations and KLT Orthogonality

TL;DR

This paper introduces scattering equations linking kinematic invariants and puncture locations, providing an inductive solution method and revealing KLT orthogonality, which has implications for gauge and gravity amplitudes across dimensions.

Contribution

It identifies the scattering equations, develops an inductive algorithm for their solutions, and proves KLT orthogonality, advancing the understanding of scattering amplitudes in various theories.

Findings

Solutions to scattering equations can be constructed inductively.

Parke-Taylor vectors from solutions are orthogonal under KLT bilinear form.

KLT orthogonality links to gauge and gravity amplitude structures.

Abstract

Several recent developments point to the fact that rational maps from n-punctured spheres to the null cone of D dimensional momentum space provide a natural language for describing the scattering of massless particles in D dimensions. In this note we identify and study equations relating the kinematic invariants and the puncture locations, which we call the scattering equations. We provide an inductive algorithm in the number of particles for their solutions and prove a remarkable property which we call KLT Orthogonality. In a nutshell, KLT orthogonality means that "Parke-Taylor" vectors constructed from the solutions to the scattering equations are mutually orthogonal with respect to the Kawai-Lewellen-Tye (KLT) bilinear form. We end with comments on possible connections to gauge theory and gravity amplitudes in any dimension and to the high-energy limit of string theory amplitudes.