On genera of curves from high-loop generalized unitarity cuts

  • Rijun Huang
  • Yang Zhang


Generalized unitarity cut of a Feynman diagram generates an algebraic system of polynomial equations. At high-loop levels, these equations may define a complex curve or a (hyper-)surface with complicated topology. We study the curve cases, i.e., a 4-dimensional L-loop diagram with (4L−1) cuts. The topology of a complex curve is classified by its genus. Hence in this paper, we use computational algebraic geometry to calculate the genera of curves from two and three-loop unitarity cuts. The global structure of degenerate on-shell equations under some specific kinematic configurations is also sketched. The genus information can also be used to judge if a unitary cut solution could be rationally parameterized.


Scattering Amplitudes QCD Differential and Algebraic Geometry 


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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Niels Bohr International Academy and Discovery CenterThe Niels Bohr InstituteCopenhagen ØDenmark

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