Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory

N. Emil J. Bjerrum-Bohr, Tristan Dennen, Ricardo Monteiro, Donal O'Connell

Research output: Contribution to journalArticlepeer-review


We present a systematic method to determine BCJ numerators for one-loop amplitudes that explores the global constraints on the loop momentum dependence. We apply this method to amplitudes in N=4 gauge theory, working out detailed examples up to seven points in both the MHV and the NMHV sectors. The structure of Jacobi identities between BCJ numerators is seen to be closely connected to that of algebraic integrand reductions. We discuss the consequences for one-loop N=8 supergravity amplitudes obtained through the double copy prescription. Moreover, in the MHV sector, we show how to obtain simple BCJ box numerators using a conjectured relationship to amplitudes in self-dual gauge theory. We also introduce simpler trace-type formulas for integrand reductions.
Original languageEnglish
Article number92
JournalJournal of High Energy Physics
Issue number07
Early online date12 Mar 2013
Publication statusPublished - 15 Jul 2013


  • hep-th
  • Scattering Amplitudes
  • Extended Supersymmetry


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