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In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.
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Zvi Bern
John Joseph M. Carrasco
Henrik Johansson
Physical Review Letters
University of California, Los Angeles
Commissariat à l'Énergie Atomique et aux Énergies Alternatives
CEA Paris-Saclay
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Bern et al. (Tue,) studied this question.
www.synapsesocial.com/papers/69db1d75498b35d3e6a3c72d — DOI: https://doi.org/10.1103/physrevlett.105.061602