Color structures and permutations

Barak Kol, Ruth Shir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Color structures for tree level scattering amplitudes in gauge theory are studied in order to determine the symmetry properties of the color-ordered sub-amplitudes. We mathematically formulate the space of color structures together with the action of permuting external legs. The character generating functions are presented from the mathematical literature and we determine the decomposition into irreducible representations. Mathematically, free Lie algebras and the Lie operad are central. A study of the implications for sub-amplitudes is initiated and we prove directly that both the Parke-Taylor amplitudes and Cachazo-He-Yuan amplitudes satisfy the Kleiss-Kuijf relations.

Original languageAmerican English
Article number20
JournalJournal of High Energy Physics
Issue number11
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2014, The Author(s).


  • 1/N expansion
  • Gauge symmetry
  • Scattering amplitudes


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