Color structures and permutations
Abstract
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.
Cite
@article{arxiv.1403.6837,
title = {Color structures and permutations},
author = {Barak Kol and Ruth Shir},
journal= {arXiv preprint arXiv:1403.6837},
year = {2015}
}
Comments
22 pages. v2: minor changes. v3: JHEP published version. Additional examples and explanations