Algebras for Amplitudes
N. E. J. Bjerrum-Bohr, Poul H. Damgaard, Ricardo Monteiro, Donal, O'Connell
TL;DR
This paper introduces a new formalism for gauge theory amplitudes that explicitly factorizes color and kinematics, clarifies the color-kinematics duality, and relates gravity amplitudes to gauge theory bases using KK and BCJ relations.
Contribution
It presents a basis of gauge theory amplitudes with cubic vertices that makes color-kinematics duality explicit and connects gravity amplitudes through permutation-symmetric coefficients.
Findings
Explicit factorization of vertices in color and kinematics
Clarification of the role of KK and BCJ relations
Expression of gravity amplitudes via gauge theory bases
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.
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