String-inspired BCJ numerators for one-loop MHV amplitudes

TL;DR

This paper derives simple, universal expressions for one-loop MHV amplitudes in supersymmetric gauge and gravity theories, demonstrating BCJ duality and connecting self-dual and maximally supersymmetric cases.

Contribution

It provides explicit BCJ numerators for one-loop MHV amplitudes in supersymmetric theories, highlighting their structure and relation to self-dual theories.

Findings

BCJ numerators satisfy color-kinematics duality

Gravity numerators are squares of gauge theory numerators

Connection between self-dual and maximally supersymmetric amplitudes

Abstract

We find simple expressions for the kinematic numerators of one-loop MHV amplitudes in maximally supersymmetric Yang-Mills theory and supergravity, for any multiplicity. The gauge theory numerators satisfy the Bern-Carrasco-Johansson (BCJ) duality between color and kinematics, so that the gravity numerators are simply the square of the gauge theory ones. The duality holds because the numerators can be written in terms of structure constants of a kinematic algebra, which is familiar from the BCJ organization of self-dual gauge theory and gravity. The close connection that we find between one-loop amplitudes in the self-dual case and in the maximally supersymmetric case is the converse to the dimension-shifting formula. The starting point for arriving at our expressions is the dimensional reduction of ten-dimensional amplitudes obtained in the field-theory limit of open superstrings.