Loop Integrands for Scattering Amplitudes from the Riemann Sphere.

  title={Loop Integrands for Scattering Amplitudes from the Riemann Sphere.},
  author={Yvonne Geyer and Lionel Mason and Ricardo Monteiro and Piotr Tourkine},
  journal={Physical review letters},
  volume={115 12},
The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have a wide application, based on off-shell scattering equations that… 

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