Note on Construction of Dual-trace Factor in Yang-Mills Theory

Abstract

In this note we provide a new construction of BCJ dual-trace factor using the kinematic algebra proposed in arXiv:1105.2565 and arXiv:1212.6168. Different from the construction given in arXiv:1304.2978 based on the proposal of arXiv:1103.0312, the method used in this note exploits the adjoint representation of kinematic algebra and the use of inner product in dual space. The dual-trace factor defined in this way naturally satisfies cyclic symmetry condition but not KK-relation, just like the trace of U(N) Lie algebra satisfies cyclic symmetry condition, but not KK-relation. In other words the new construction naturally leads to formulation sharing more similarities with the color decomposition of Yang-Mills amplitude.

15 pages, improved version

References in corpus (5)

• Minimal Basis for Gauge Theory Amplitudes
• The Kinematic Algebra From the Self-Dual Sector
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• New Identities among Gauge Theory Amplitudes

Cited by in corpus (13)

• Black holes and the double copy
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• The Kerr-Schild double copy in curved spacetime
• The Kinematic Algebras from the Scattering Equations
• Amplitude Relations in Non-linear Sigma Model
• Expansion of Einstein-Yang-Mills Amplitude
• Double-Copy Constructions and Unitarity Cuts
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• Dual-color decompositions at one-loop level in Yang-Mills theory
• Note on symmetric BCJ numerator
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• The seeds of EFT double copy