Abstract
We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory.For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/□ is replaced with covariant 1/D2. Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background.Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.
Highlights
Color-kinematics duality is an astonishing property of scattering amplitudes that links vastly disparate phenomena in nature: gravitation and the strong interactions
We have shown from first principles how YM theory is the covariant double copy of gauged biadjoint scalar (GBAS) theory and F 3 theory
We have derived a formulation of color-kinematics duality and the double copy implemented at the level of fields and equations of motion
Summary
Color-kinematics duality is an astonishing property of scattering amplitudes that links vastly disparate phenomena in nature: gravitation and the strong interactions. The ultimate aspiration might be to derive color-kinematics duality directly from the known textbook formulations of the double copy theories To this end we achieve partial progress: color-kinematics duality — or at least some variant of it — can be made manifest at the level of equations of motion provided one recasts the dynamics in terms of currents and field strengths rather than the traditional underlying degrees of freedom. This description exhibits manifest color-kinematics duality, which is why its associated Feynman rules satisfy the kinematic Jacobi identities automatically. In appendix B we present a simple derivation of the fundamental BCJ relations using equations of motion
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
