Scattering equations and virtuous kinematic numerators and dual-trace functions

TL;DR

This paper introduces a constructive method to compute symmetric, amplitude-encoded BCJ numerators and dual-trace functions for n-point gauge-theory and gravity amplitudes, ensuring color-kinematic duality and manifest S_n symmetry.

Contribution

It provides explicit procedures for symmetric, amplitude-encoded kinematic numerators and dual-trace functions, advancing the computation of gauge and gravity amplitudes with desired symmetries.

Findings

Explicit four- and five-point amplitude expressions

Symmetric dual-trace functions satisfy color-kinematic duality

Manifest S_n symmetry in gravity amplitudes

Abstract

Inspired by recent developments on scattering equations, we present a constructive procedure for computing symmetric, amplitude-encoded, BCJ numerators for n-point gauge-theory amplitudes, thus satisfying the three virtues identified by Broedel and Carrasco. We also develop a constructive procedure for computing symmetric, amplitude-encoded dual-trace functions (tau) for n-point amplitudes. These can be used to obtain symmetric kinematic numerators that automatically satisfy color-kinematic duality. The S_n symmetry of n-point gravity amplitudes formed from these symmetric dual-trace functions is completely manifest. Explicit expressions for four- and five-point amplitudes are presented.