Berends-Giele recursion for double-color-ordered amplitudes

TL;DR

This paper extends Berends-Giele recursion to double-color-ordered amplitudes in bi-adjoint scalar theory, providing new computational tools and insights into KLT matrices and BCJ numerators.

Contribution

It generalizes Berends-Giele currents to double-currents and derives their recursions, linking them to KLT matrices and string amplitude limits.

Findings

Inverse KLT matrix entries equal to Berends-Giele double-currents

Derived a simple formula for BCJ-satisfying numerators

Validated methods through applications to string amplitudes

Abstract

Tree-level double-color-ordered amplitudes are computed using Berends--Giele recursion relations applied to the bi-adjoint cubic scalar theory. The standard notion of Berends--Giele currents is generalized to double-currents and their recursions are derived from a perturbiner expansion of linearized fields that solve the non-linear field equations. Two applications are given. Firstly, we prove that the entries of the inverse KLT matrix are equal to Berends--Giele double-currents (and are therefore easy to compute). And secondly, a simple formula to generate tree-level BCJ-satisfying numerators for arbitrary multiplicity is proposed by evaluating the field-theory limit of tree-level string amplitudes for various color orderings using double-color-ordered amplitudes.