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 (23)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Multi-Parton Amplitudes in Gauge Theories
• Scattering of Massless Particles in Arbitrary Dimension
• The Amplituhedron
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Minimal Basis for Gauge Theory Amplitudes
• Progress in One-Loop QCD Computations
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• Open & Closed vs. Pure Open String Disk Amplitudes
• The Grassmannian Origin Of Dual Superconformal Invariance
• Algebras for Amplitudes
• Scattering amplitudes: the most perfect microscopic structures in the universe
• A simple formula for gravitational MHV amplitudes
• Orthogonal multiplet bases in SU(Nc) color space
• A dictionary between R-operators, on-shell graphs and Yangian algebras
• Decomposition of one-loop QCD amplitudes into primitive amplitudes based on shuffle relations
• Comment on the Identities of the Gluon Tree Amplitudes
• Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes
• Koszul duality for Operads
• A Shortcut to General Tree-level Scattering Amplitudes in N=4 SYM via Integrability

Cited by in corpus (11)

• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• CHY formula and MHV amplitudes
• Perturbative Quantum Field Theory and Homotopy Algebras
• Planar Zeros in Gauge Theories and Gravity
• Perturbative gauge theory and 2+2=4
• On a generalization of Lie($k$): a CataLAnKe theorem
• 1-loop Color structures and sunny diagrams
• Recursion in multiplet bases for tree-level MHV gluon amplitudes