A study in 𝔾ℝ,≥0: from the geometric case book of Wilson loop diagrams and SYM N=4

@article{Agarwala2022ASI,
  title={A study in 𝔾ℝ,≥0: from the geometric case book of Wilson loop diagrams and SYM N=4},
  author={Susama Agarwala and Zee Fryer},
  journal={Annales de l’Institut Henri Poincar{\'e} D},
  year={2022}
}
We study the geometry underlying the Wilson loop diagram approach to calculating scattering amplitudes in the gauge theory of Supersymmetric Yang Mills (SYM) N=4. By applying the tools developed to study total positivity in the real Grassmannian, we are able to systematically compute with all Wilson loop diagrams of a given size and find unexpected patterns and relationships between them. We focus on the smallest nontrivial multi-propagator case, consisting of 2 propagators on 6 vertices, and… 
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19 References

Wilson Loop Diagrams and Positroids

In this paper, we study a new application of the positive Grassmannian to Wilson loop diagrams (or MHV diagrams) for scattering amplitudes in N= 4 Super Yang–Mill theory (N = 4 SYM). There has been…

Grassmannian Geometry of Scattering Amplitudes

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