This review describes the duality between color and kinematics and its applications, with the
aim of gaining a deeper understanding of the perturbative structure of gauge and gravity …

A bstract The search for a theory of the S-Matrix over the past five decades has revealed
surprising geometric structures underlying scattering amplitudes ranging from the string …

The duality between color and kinematics was originally observed for purely adjoint
massless gauge theories, and later found to hold even after introducing massive fermionic …

A bstract Recent years have seen the emergence of a new understanding of scattering
amplitudes in the simplest theory of colored scalar particles—the Tr (ϕ 3) theory—based on …

We present a closed formula for all Bern-Carrasco-Johansson (BCJ) numerators describing
D-dimensional tree-level scattering amplitudes in a heavy-mass effective field theory with …

We perturbatively calculate classical radiation in Yang-Mills theory and dilaton gravity, to
next-to-leading order in couplings. The radiation is sourced by the scattering of two …

A bstract 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 …

A bstract We derive new amplitudes relations revealing a hidden unity among a wideranging
variety of theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz …

We use the recently developed generalized double-copy procedure to construct an
integrand for the five-loop four-point amplitude of N= 8 supergravity. This construction starts …

A bstract Using the double-copy construction of Yang-Mills-Einstein theories formulated in
our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree …