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.
Highlights
It is truly surprising that, more than sixty years after the basic principles of quantum field theory have been spelled out, we continue to discover profound facts about its perturbative expansion
In this work we have studied the kinematic monodromy relations on single cuts of one-loop amplitudes in gauge theory
These relations are derived from the monodromy relations on the regularised forward tree amplitudes
Summary
It is truly surprising that, more than sixty years after the basic principles of quantum field theory have been spelled out, we continue to discover profound facts about its perturbative expansion. This leads us to some relations between regularised forward tree-amplitudes, somehow similar to these of [26, 27] based on the Cachazo, He and Yuan formalism (CHY) [28, 29]. We further show on a few examples how these integrand relations are always satisfied if a colour-dual representation of the loop amplitude exists.
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