1-loop color structures and sunny diagrams

Barak Kol, Ruth Shir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The space of tree level color structures for gluon scattering was determined recently along with its transformation properties under permutations. Here we generalize the discussion to loops, demonstrating a reduction of an arbitrary color diagram to its vacuum skeleton plus rays. For 1-loop there are no residual relations and we determine the space of color structures both diagrammatically and algebraically in terms of certain sunny diagrams. We present the generating function for the characteristic polynomials and a list of irreducible representations for 3 ≤ n ≤ 9 external legs. Finally we present a new proof for the 1-loop shuffle relations based on the cyclic shuffle and split operations.

Original languageAmerican English
Article number85
JournalJournal of High Energy Physics
Issue number2
StatePublished - Feb 2015

Bibliographical note

Publisher Copyright:
© 2015, The Author(s).


  • 1/N Expansion
  • Gauge Symmetry
  • Scattering Amplitudes


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