Abstract
Color-kinematics duality is a remarkable conjectured property of gauge theory which, together with double copy, is at the heart of a wealth of new developments in scattering amplitudes. So far, its validity has been verified in most cases only empirically, with limited ab initio understanding beyond tree-level. In this paper we provide initial steps in a first-principle understanding of color-kinematics duality and double-copy at loop level, through a detailed analysis of the field-theory limit of the monodromy relations of string theory at one loop. In this limit, we dissect the type of Feynman graphs generated and the relations they obey. We find that graphs with contact-terms are unavoidable and are generated in the field theory limit of “bulk” contours which do not have a standard physical interpretation in string perturbation theory. We show how they are related to ambiguities in the definition of the loop momentum and that their role is precisely to cancel those ambiguities.
Highlights
Our approach to this problem, which has proven useful in the past, will be to use string theory
It originates from fundamental identities in open-string theory scattering amplitudes, known since the early days of dual models [11], today known as monodromy relations [4, 5, 11,12,13]
Over the past few years a related approach based on ambitwistor string theory has emerged, see, e.g., [21,22,23,24,25,26,27], which gives a handle on the problem of constructing BCJ numerators, at a cost of introducing linearized propagators which need to be transformed into quadratic ones using non-trivial partial fraction identities
Summary
We find that the field theory limit of the monodromy relations produces numerators which automatically satisfy Jacobi identities inside the graph, i.e., in those places where the definition of the loop momentum would not be changed by a Jacobi move, as explained above. We characterize the extra contributions arising from the bulk transverse integrals of the annulus present in the monodromy relations We carefully compute their field theory limit and show that it produces two types of graphs: contact terms, and graphs with trees attached to the loop. This can be seen as a new item in the Bern-Kosower rules, required for the monodromy relations.
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