Perfecting one-loop BCJ numerators in SYM and supergravity

TL;DR

This paper advances the computation of one-loop amplitudes in gauge theories by providing explicit, all-multiplicity numerators that satisfy color-kinematics duality, locality, and compatibility with double copy, for various supersymmetric and non-supersymmetric cases.

Contribution

It introduces new all-multiplicity expressions for kinematic numerators that realize color-kinematics duality and contact terms for n-point amplitudes, including solutions for six and seven points with maximal supersymmetry.

Findings

Derived explicit maximal cut expressions for n-point amplitudes.

Extended numerators to encode contact terms at 6 and 7 points with supersymmetry.

Confirmed ultraviolet divergence predictions through double copy constructions.

Abstract

We take a major step towards computing $D$-dimensional one-loop amplitudes in general gauge theories, compatible with the principles of unitarity and the color-kinematics duality. For $n$-point amplitudes with either supersymmetry multiplets or generic non-supersymmetric matter in the loop, simple all-multiplicity expressions are obtained for the maximal cuts of kinematic numerators of $n$-gon diagrams. At $n=6,7$ points with maximal supersymmetry, we extend the cubic-diagram numerators to encode all contact terms, and thus solve the long-standing problem of \emph{simultaneously} realizing the following properties: color-kinematics duality, manifest locality, optimal power counting of loop momenta, quadratic rather than linearized Feynman propagators, compatibility with double copy as well as all graph symmetries. Color-kinematics dual representations with similar properties are presented in the half-maximally supersymmetric case at $n=4,5$ points. The resulting gauge-theory integrands and their supergravity counterparts obtained from the double copy are checked to reproduce the expected ultraviolet divergences.