Related papers: A Lie bracket for the momentum kernel
Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this paper we introduce new double-copy constructions for large…
Tree-level amplitudes of gauge theories are expressed in a basis of auxiliary amplitudes with only cubic vertices. The vertices in this formalism are explicitly factorized in color and kinematics, clarifying the color-kinematics duality in…
Conventional Lagrangian formulations of gauge and gravity theories emphasize compactness and off-shell symmetry. This often obscures the structure of on-shell physical observables. In this work, we present a constructive framework that…
Here we discuss color-kinematics duality for higher-derivative QCD-like amplitudes. We explicitly show that the duality still holds in this case and it can be instrumental in constructing the associated quadratic-gravity amplitudes by using…
We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color…
We demonstrate that modern machine-learning methods can autonomously reconstruct several flagship analytic structures in scattering amplitudes directly from numerical on-shell data. In particular, we show that the Kawai--Lewellen--Tye (KLT)…
Based on the covariant color-kinematics duality, we investigate combinatorial and algebraic structures underlying their Bern-Carrasco-Johansson (BCJ) numerators of tree-level amplitudes in Yang-Mills-scalar (YMS) theory. The closed-formulae…
Recently it has been shown that Bern-Carrasco-Johansson (BCJ) numerators of colour-kinematic duality for tree-level scattering amplitudes in Yang-Mills theory (coupled with scalars) can be determined using a quasi-shuffle Hopf algebra. In…
In flat space, the color/kinematics duality states that perturbative Yang-Mills amplitudes can be written in such a way that kinematic numerators obey the same Jacobi relations as their color factors. This remarkable duality implies BCJ…
We formalize the computation of tree-level scattering amplitudes in terms of the homotopy transfer of homotopy algebras, illustrating it with scalar $\phi^3$ and Yang-Mills theory. The data of a (gauge) field theory with an action is…
Both the Bern, Carrasco and Johansson (BCJ) and the Kawai, Lewellen and Tye (KLT) double-copy formalisms have been recently generalized to a class of scattering matrix elements (so-called form factors) that involve local gauge-invariant…
The double copy programme relies crucially on the so-called color-kinematics duality which, in turn, is widely believed to descend from a kinematic algebra possessed by gauge theories. In this paper we construct the kinematic algebra of…
We extend the double copy picture of scattering amplitudes to a class of matrix elements (so-called form factors) that involve local gauge invariant operators. Both the Bern, Carrasco and Johansson (BCJ) and the Kawai, Lewellen and Tye…
The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over an Euclidean space. In this article, we review the last developments concerning…
A new perspective on the inverse string theory Kawai-Lewellen-Tye (KLT) kernel is provided which establishes the universality of scattering amplitudes in the bi-adjoint scalar (BAS) theory, pions in the Non-linear sigma model (NLSM), and…
The discovery of colour-kinematic duality has led to significant progress in the computation of scattering amplitudes in quantum field theories. At tree level, the origin of the duality can be traced back to the monodromies of open-string…
Recently, Arkani-Hamed et al. proposed the existence of zeros in scattering amplitudes in certain quantum field theories including the cubic adjoint scalar theory Tr($\phi^3$), the $SU(N)$ non-linear sigma model (NLSM) and Yang-Mills (YM)…
We derive a vertex operator based expression for the kinematic numerators of Yang-Mills amplitudes by applying the momentum kernel formalism to open string amplitudes. The expression involves an $\alpha'$-weighted commutator induced by the…
The Bern-Carrasco-Johansson (BCJ) double-copy construction reveals a fundamental structural connection between gauge and gravity theories. At its core, the BCJ double copy is directly due to a duality between the algebraic relations of a…
Recently a powerful duality between color and kinematics has been proposed for integrands of scattering amplitudes in quite general gauge theories. In this paper the duality proposal is extended to the more general class of gauge theory…