Local BCJ numerators for ten-dimensional SYM at one loop

TL;DR

This paper derives explicit local BCJ numerators satisfying color-kinematics duality at one loop for ten-dimensional super-Yang-Mills theory, resolving previous issues at six points by connecting string theory correlators to field theory.

Contribution

It provides the first explicit construction of one-loop local BCJ numerators in ten-dimensional SYM, extending tree-level results to loop level using string theory techniques.

Findings

Explicit six-point one-loop numerators satisfying BCJ duality

Resolution of previous puzzles regarding six-point numerators

Connection between string correlators and field theory numerators

Abstract

We obtain local numerators satisfying the BCJ color-kinematics duality at one loop for super-Yang-Mills theory in ten dimensions. This is done explicitly for six points via the field-theory limit of the genus-one open superstring correlators for different color orderings, in an analogous manner to an earlier derivation of local BCJ-satisfying numerators at tree level from disk correlators. These results solve an outstanding puzzle from a previous analysis where the six-point numerators did not satisfy the color-kinematics duality.