One-loop monodromy relations on single cuts

TL;DR

This paper explores one-loop monodromy relations in quantum field theory, revealing new classes of amplitudes and clarifying the role of momentum-shifting ambiguities through string-theoretic analysis.

Contribution

It extends monodromy relations to one-loop amplitudes, identifying new independent classes and analyzing their implications for color-kinematic duality.

Findings

Identification of new kinematically independent single-cut amplitudes

Revisiting string-theoretic derivation clarifies momentum-shifting ambiguities

Compatibility of color-dual representations with monodromy relations

Abstract

The discovery of colour-kinematic duality has led to significant progress in the computation of scattering amplitudes in quantum field theories. At tree level, the origin of the duality can be traced back to the monodromies of open-string amplitudes. This construction has recently been extended to all loop orders. In the present paper, we dissect some consequences of these new monodromy relations at one loop. We use single cuts in order to relate them to the tree-level relations. We show that there are new classes of kinematically independent single-cut amplitudes. Then we turn to the Feynman diagrammatics of the string-theory monodromy relations. We revisit the string-theoretic derivation and argue that some terms, that vanish upon integration in string and field theory, provide a characterisation of momentum-shifting ambiguities in these representations. We observe that colour-dual representations are compatible with this analysis.