D=5 maximally supersymmetric Yang-Mills theory diverges at six loops

Zvi Bern*, John Joseph Carrasco, Lance J. Dixon, Michael R. Douglas, Matt Von Hippel, Henrik Johansson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large Nc) maximally supersymmetric Yang-Mills theory in D=5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L>6 in the critical dimension D=4+6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. The vacuum integrals are integrated via sector decomposition, using a modified version of the FIESTA program.

Original languageEnglish (US)
Article number025018
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
StatePublished - Jan 14 2013

ASJC Scopus subject areas

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


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