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

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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 ... continued below

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48 pages

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Bern, Z.; Dixon, L.J.; Kosower, D.A.; Roiban, R.; Spradlin, M.; Vergu, C. et al. March 12, 2008.

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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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48 pages

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  • Journal Name: Physical Review D

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  • Report No.: SLAC-PUB-13150
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 925454
  • Archival Resource Key: ark:/67531/metadc892966

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  • March 12, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Dec. 2, 2016, 4:22 p.m.

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Bern, Z.; Dixon, L.J.; Kosower, D.A.; Roiban, R.; Spradlin, M.; Vergu, C. et al. The Two-Loop Six-Point MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, article, March 12, 2008; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc892966/: accessed December 12, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.