Abstract
Abstract 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 gauge theory amplitudes. The basis is constructed making use of the KK and BCJ relations, thereby showing precisely how these relations underlie the color-kinematics duality. We express gravity amplitudes in terms of a related basis of color-dressed gauge theory amplitudes, with basis coefficients which are permutation symmetric.
Highlights
It was found that scattering amplitudes can be written such that the color-kinematics duality is satisfied, and that this implies the existence of certain linear relations between color-ordered amplitudes, known as the BCJ relations
Comparing with the expression (5.1), we can see that the kinematic prefactors τ(1,2,...,n) play the same role for gravity amplitudes as the color traces play for gauge theory amplitudes
We have presented a systematic way to express tree-level gauge theory amplitudes in a manifest color-kinematics dual representation
Summary
Where the T a’s denote the fundamental representation matrices of the Lie gauge group, and the sum is over non-cyclic permutations of external legs. The gauge invariant components A(1, 2, . . . , n) are referred to as color-ordered amplitudes. The BCJ relations were obtained in [2] as a result of a surprising property of gauge theory amplitudes: that they can always be written as a sum over diagrams with only cubic. Vertices, the cubic structure being determined by the color factors appearing at each vertex:. There is a duality between color and kinematics The fact that this representation is possible for gauge theory amplitudes (and for amplitudes of the closely related theories to be discussed ) implies linear relations among color-ordered amplitudes, the BCJ relations. While the color factors ci follow straightforwardly from sewing together the structure constants f abc for each diagram with cubic vertices, the numerators ni are not given a vertex interpretation. We will use these results as a guide to understand the general case
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