  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.
