# 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…

## 5 Citations

### Wilson loops in SYM $N=4$ do not parametrize an orientable space

- Mathematics
- 2018

In this paper we explore the geometric space parametrized by (tree level) Wilson loops in SYM $N=4$. We show that, this space can be seen as a vector bundle over a totally non-negative subspace of…

### The twistor Wilson loop and the amplituhedron

- PhysicsJournal of High Energy Physics
- 2018

A bstractThe amplituhedron provides a beautiful description of perturbative superamplitude integrands in N=4$$ \mathcal{N}=4 $$ SYM in terms of purely geometric objects, generalisations of polytopes.…

### Basis shape loci and the positive Grassmannian

- Mathematics
- 2019

A basis shape locus takes as input data a zero/nonzero pattern in an $n \times k$ matrix, which is equivalent to a presentation of a transversal matroid. The locus is defined as the set of points in…

### AN ALGORITHM TO CONSTRUCT THE LE DIAGRAM ASSOCIATED TO A GRASSMANN NECKLACE

- MathematicsGlasgow Mathematical Journal
- 2019

Abstract Le diagrams and Grassmann necklaces both index the collection of positroids in the nonnegative Grassmannian Gr≥0(k, n), but they excel at very different tasks: for example, the dimension of…

### Quotients of Uniform Positroids

- MathematicsElectron. J. Comb.
- 2022

Two matroids $M$ and $N$ are said to be concordant if there is a strong map from $N$ to $M$. This also can be stated by saying that each circuit of $N$ is a union of circuits of $M$. In this paper,…

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