Covariant color-kinematics duality

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.

Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory

“…which is in agreement with [15]. Finally, we remark that our BCJ numerators for npoint pure YM amplitudes have some similarity with those given in [40]. Both constructions maintain gauge invariance and crossing symmetry of n−1 external legs, and contain linear spurious poles.…”

Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles

“…[22,44,[50][51][52][53][54]). The question we ask here is, however, can we demystify these relations purely from field-theory perspective (see [55,56])?…”

The off-shell recursion for gravity and the classical double copy for currents

“…Mizera and Skrzypek proposed the KLT relation for off-shell currents of the non-gravitational effective field theories [93]. Recently Cheung and Mangan introduced a map between gluon and graviton currents based on the color-kinematic duality [96]. Then we will present the current KLT relation for gravity by using the explicit form of the gluon and graviton currents.…”

“…Therefore, the perturbiner method that does not use the Feynman vertices is suitable in developing the off-shell recursion for gravity. Recently, there have been several works deriving the graviton off-shell recursions from the perturbative GR [32,33,95,96], and the associated graviton off-shell currents have been obtained using the recursions.…”

“…Remarkably, the graviton currents exhibit the current KLT relation, representing the graviton currents by the square of gluon currents. Recently, the current KLT relation for the non-gravitational effective theories are studied in [93], and the color-kinematic duality for the off-shell currents is introduced in [96]. Comparing with the non-gravitational current KLT relation, the gravitational case contains contributions from the regular terms for the propagators of the off-shell leg, which do not contribute to the scattering amplitudes.…”