Loop amplitudes monodromy relations and color-kinematics duality

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, lacking a first-principle 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.

arXiv comment26 pages, 15 figures. Figures in IPE (http://ipe.otfried.org/). v2: clarified discussions, added a few references. Published version

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• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Tree-level amplitudes from the pure spinor superstring
• Superstring loop amplitudes from the field theory limit
• Towards Color-Kinematics Duality in Generic Spacetimes
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Unitarity Cuts of the Worldsheet
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Color-kinematics duality from the Bern-Kosower formalism
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Local BCJ numerators for ten-dimensional SYM at one loop
• Worldline description of a bi-adjoint scalar and the zeroth copy
• A double copy from twisted (co)homology at genus one
• Basis decompositions of genus-one string integrals
• Advanced tools for basis decompositions of genus-one string integrals
• Next-to-MHV Yang-Mills kinematic algebra
• One-loop four-graviton string amplitude at finite ${\alpha }^{\prime }$
• Twisted de Rham theory for string double copy in AdS