Abstract
We present a world-sheet formula for all tree level scattering amplitudes, in all trace sectors, of four dimensional \( \mathcal{N}\le 4 \) supersymmetric Einstein-Yang-Mills theory, based on the refined scattering equations. This generalizes previously known formulas for all-trace purely bosonic, or supersymmetric single-trace amplitudes. We find this formula by applying a new chiral splitting formula for all CHY Pfaffians in 4d, into two determinants, of positive and negative helicity respectively. The splitting of CHY Pfaffians is shown to be a special case of the splitting of \( T\mathbb{M} \) valued fermion correlators on the sphere, which does not require the scattering equations to hold, and is a consequence of the isomorphism \( T\mathbb{M}\simeq {\mathbb{S}}^{+}\otimes {\mathbb{S}}^{-} \) between the tangent bundle of Minkowski space and the left- and right-handed spin bundles. We present and prove this general splitting formula.
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Roehrig, K.A. Chiral splitting and \( \mathcal{N}=4 \) Einstein-Yang-Mills tree amplitudes in 4d. J. High Energ. Phys. 2017, 33 (2017). https://doi.org/10.1007/JHEP08(2017)033
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DOI: https://doi.org/10.1007/JHEP08(2017)033