New relations for gauge-theory amplitudes

Z. Bern*, John Joseph Carrasco, H. Johansson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

808 Scopus citations


We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.

Original languageEnglish (US)
Article number085011
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number8
StatePublished - Oct 16 2008

ASJC Scopus subject areas

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


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