Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory

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...

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Bibliographic Details
Published in:Physical review letters 2016-11, Vol.117 (21), p.211601-211601, Article 211601
Main Authors: Tourkine, Piotr, Vanhove, Pierre
Format: Article
Language:English
Subjects:
Amplitudes
Contours
Field theory
Formalism
High Energy Physics - Theory
Physics
Quantum theory
Shape
String theory
Strings
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.117.211601