title: Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory.
abstract: The monodromy relations in string theory provide a powerful and elegant formalism to understand some of the deepest properties of tree-level field theory amplitudes, like the color-kinematics duality. This duality has been instrumental in tremendous progress on the computations of loop amplitudes in quantum field theory, but a higher-loop generalization of the monodromy construction was lacking. In this Letter, we extend the monodromy relations to higher loops in open string theory. Our construction, based on a contour deformation argument of the open string diagram integrands, leads to new identities that relate planar and nonplanar topologies in string theory. We write one and two-loop monodromy formulas explicitly at any multiplicity. In the field theory limit, at one-loop we obtain identities that reproduce known results. At two loops, we check our formulas by unitarity in the case of the four-point N=4 super-Yang-Mills amplitude.
authors.affiliation: DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
authors.forename: Piotr
authors.initials: P
authors.lastname: Tourkine
authors.affiliation: DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.|Institut de physique théorique, Université Paris Saclay, CNRS, F-91191 Gif-sur-Yvette, France.
authors.forename: Pierre
authors.initials: P
authors.lastname: Vanhove