Monodromy--like Relations for Finite Loop Amplitudes

TL;DR

The paper investigates hidden, monodromy-like relations among finite one-loop Yang-Mills amplitudes, focusing on all-plus and one-minus helicity configurations. It introduces a diagrammatic framework with a single symmetric quartic vertex and antisymmetric cubic vertices to derive KK-like relations for all-plus amplitudes, and extends the construction to one-minus amplitudes by incorporating an effective cubic vertex. The authors show substantial reduction in independent amplitudes, suggest connections to tree-level BCJ/monodromy structures, and propose a unified, potentially string-theoretic origin for these relations. They also discuss higher-point, helicity-specific relations and outline future directions, including extensions to divergent parts and rational pieces.

Abstract

We investigate the existence of relations for finite one-loop amplitudes in Yang-Mills theory. Using a diagrammatic formalism and a remarkable connection between tree and loop level, we deduce sequences of amplitude relations for any number of external legs.