Explicit BCJ numerators of nonlinear sigma model

Abstract

In this paper, we investigate the color-kinematics duality in nonlinear sigma model (NLSM). We present explicit polynomial expressions for the kinematic numerators (BCJ numerators). The calculation is done separately in two parametrization schemes of the theory using Kawai-Lewellen-Tye relation inspired technique, both lead to polynomial numerators. We summarize the calculation in each case into a set of rules that generates BCJ numerators for all multilplicities. In Cayley parametrization we find the numerator is described by a particularly simple formula solely in terms of momentum kernel.

32 pages, 2 figures; v2: typos fixed, references added, matches published version

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• A Lie bracket for the momentum kernel
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Tree-Level Color-Kinematics Duality Implies Loop-Level Color-Kinematics Duality up to Counterterms
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Colour-kinematics duality, double copy, and homotopy algebras
• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
• Non-Abelian gauged supergravities as double copies