Two-loop six-gluon maximally helicity violating amplitude in maximally supersymmetric Yang-Mills theory

Z. Bern, L. J. Dixon, D. A. Kosower, R. Roiban, M. Spradlin, C. Vergu, A. Volovich

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We give a representation of the parity-even part of the planar two-loop six-gluon maximally helicity violating (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 Anastasiou-Bern-Dixon-Kosower/Bern-Dixon-Smirnov 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. 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 nontrivial 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.

Original languageEnglish (US)
Article number045007
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number4
StatePublished - Aug 11 2008

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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