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Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
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abstract
We study four point planar loop amplitudes at an arbitrary point in the Coulomb branch of $\mathcal{N}=4$ super-Yang-Mills theory. We study two particle unitary cuts up to four loop order. We explicitly verify that bubble and triangle graphs do not contribute at one loop level and show that the results hold at higher loop level as well. We also write down an all loop recursion relation for two particle reducible graphs for four point amplitudes.
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Symplectic Grassmannian description of the Coulomb branch three and four point amplitudes
Three- and four-point Coulomb branch amplitudes of N=4 SYM are expressed as symplectic Grassmannian integrals over SpGr(3,6) and SpGr(4,8), up to a fitted kinematic factor at four points.
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