Wilson loops in SYM 𝒩=4 do not parametrize an orientable space
Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 4, pp. 583-622.
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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 Grassmannian, 𝒲 k,n . Furthermore, we explicitly show that this bundle is non-orientable in the majority of the cases, and conjecture that it is non-orientable in the remaining situation. Using the combinatorics of the Deodhar decomposition of the Grassmannian, we identify subspaces Σ(W)⊂𝒲 k,n for which the restricted bundle lies outside the positive Grassmannian. Finally, while probing the combinatorics of the Deodhar decomposition, we give a diagrammatic algorithm for reading equations determining each Deodhar component as a semialgebraic set.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/111
Classification : 81-XX, 14-XX
Mots-clés : SYM $\mathcal{N}=4$, positive Grassmannians, Deodhar decomposition 
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     title = {Wilson loops in {SYM} $\mathcal{N}=4$ do not parametrize an orientable space},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {583--622},
     volume = {8},
     number = {4},
     year = {2021},
     doi = {10.4171/aihpd/111},
     mrnumber = {4337449},
     zbl = {1483.81130},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/111/}
}
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Agarwala, Susama; Marcott, Cameron. Wilson loops in SYM $\mathcal{N}=4$ do not parametrize an orientable space. Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 4, pp. 583-622. doi : 10.4171/aihpd/111. http://archive.numdam.org/articles/10.4171/aihpd/111/

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