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 generalisation 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 inside open string diagrams, leads to new identities that relate planar and non-planar topologies in string theory. We write one and two-loop monodromy formulae 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 formulae by unitarity in the case of the four-point N=4 super-Yang-Mills amplitude.

6 pages, 2 figures, feynmp graphs. v2: Signs and factor 2 corrected. Various clarifications and references added. v3: Some clarifications and minor corrections, version to be published in PRL. v4: Sign corrected in non-planar phases cuts

References in corpus (5)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Worldline Green Functions for Arbitrary Feynman Diagrams

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