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.

22 pages. v2: minor changes. v3: JHEP published version. Additional examples and explanations

References in corpus (5)

• New Relations for Gauge-Theory Amplitudes
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• A simple formula for gravitational MHV amplitudes
• Koszul duality for Operads
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Cited by in corpus (5)

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• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
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• Perturbative gauge theory and 2+2=4
• Planar Zeros in Gauge Theories and Gravity