Abstract
We prove that the scattering equation formalism for Yang-Mills amplitudes can be used to make manifest the theory's color-kinematics duality. This is achieved through a concrete reduction algorithm which renders this duality manifest term-by-term. The reduction follows from the recently derived set of identities for amplitudes expressed in the scattering equation formalism that are analogous to monodromy relations in string theory. A byproduct of our algorithm is a generalization of the identities among gravity and Yang-Mills amplitudes.
Highlights
New non-trivial identities that are valid only on the support of the the scattering equations
We prove that the scattering equation formalism for Yang-Mills amplitudes can be used to make manifest the theory’s color-kinematics duality
The reduction follows from the recently derived set of identities for amplitudes expressed in the scattering equation formalism that are analogous to monodromy relations in string theory
Summary
Let us briefly review the essential ingredients for the representation of scattering amplitudes in the scattering equation formalism of CHY [1,2,3]. This is reflected in an SL(2, C) invariance in the representation of momenta in terms of the auxiliary z variables In terms of these auxiliary variables tree-level scattering amplitudes in any quantum field theory can be represented as integrals over the z’s, localized on the constraints (2.1). Color-ordered scattering amplitudes of Yang-Mills theory have an especially simple CHY-representation: AYn M(1, 2, . From the color-ordered partial amplitudes of Yang-Mills, it is easy to construct the full amplitudes This can be done, for example, using a KK-representation [23, 24] involving a reduced basis of (n − 2)! Graviton scattering amplitudes can be represented in a way that is remarkably (and suggestively) similar to the Yang-Mills squaring of KLT-relations [30]: AGn R ≡ ΩCHY (Pf Ψ). It may be worth mentioning that this remarkable representation of gravitational amplitudes, written this way first by Cachazo, He, and Yuan in [1], is a natural generalization of the formula discovered by Hodges in [31]
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