Color-kinematics duality for pure Yang-Mills and gravity at one and two loops

By Z. Bern, S. Davies, Tristan Dennen, Yu-tin Huang, Josh Nohle. 2013

157 citations recorded by the source corpus.

We provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/995f830eef48821ab5a00d51f2538d980d89ec1f

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Citations in the corpus

A two-loop five-gluon helicity amplitude in QCD (2013, methodology): “uon scattering. We would like to investigate extensions of the integrand reduction method to the non-planar where some recent developments using the colour-kinematics duality may be extremely helpful [73,74]. { 23 { Acknowledgments We are grateful to Zvi Bern, Pierpaolo Mastrolia, Simon Caron-Huot, ”
Color-kinematics duality for QCD amplitudes (2015, background): “endent primitives is reduced down to (n 3)!(2k 2)=k! for k2, and for k= 1;0 it is given by the familiar (n 3)!. The color-kinematics duality is well-established for gluons in any spacetime dimension [31,37,44], and similarly for massless particles in supersymmetric YM multiplets that comprise gluons”
Pure gravities via color-kinematics duality for fundamental matter (2014, methodology): “putation to the one with the adjoint matter. Color-kinematics dual numerators for the component amplitude with external gluons and adjoint N = 2 internal matter have already been constructed in refs. [10, 15, 28, 57]. The result presented here is a minor variation of these known forms. The main nove”
The double copy: Bremsstrahlung and accelerating black holes (2016, background): “This extension remains conjectural, but it has been verified in highly nontrivial examples at multiloop level [4, 14–35].”