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arxiv: 0803.1465 · v2 · submitted 2008-03-10 · ✦ hep-th

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The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory

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classification ✦ hep-th
keywords planaramplitudesix-gluonwilsonamplitudesansatzconformaldual
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We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N=4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal symmetry fixes their form at six points and beyond.

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  1. Form factors of $\mathscr{N}=4$ self-dual Yang-Mills from the chiral algebra bootstrap

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