Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes

TL;DR

This work analyzes monodromy relations for color-ordered amplitudes and their compatibility with Jacobi-like (BCJ) relations, showing that a broad class of generalized Jacobi identities can coexist with monodromy constraints. It connects open-string monodromy to field-theory KK/BCJ relations, and uses this structure to derive streamlined gravity amplitudes via KLT, including four- and five-point cases. The authors extend these ideas to loop-level via unitarity cuts in $ ext{N}=4$ SYM, deriving explicit one-loop coefficient relations (e.g., for six-point amplitudes) and illustrating how tree-level monodromy propagates to loop identities. Overall, the results provide a unified framework linking string-theoretic monodromy, gauge-theory color-ordered amplitudes, and gravity via KLT, with practical implications for simplifying both tree and loop computations.

Abstract

We discuss monodromy relations between different color-ordered amplitudes in gauge theories. We show that Jacobi-like relations of Bern, Carrasco and Johansson can be introduced in a manner that is compatible with these monodromy relations. The Jacobi-like relations are not the most general set of equations that satisfy this criterion. Applications to supergravity amplitudes follow straightforwardly through the KLT-relations. We explicitly show how the tree-level relations give rise to non-trivial identities at loop level.