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.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

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 
@article{AIHPD_2021__8_4_583_0,
     author = {Agarwala, Susama and Marcott, Cameron},
     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://www.numdam.org/articles/10.4171/aihpd/111/}
}
TY  - JOUR
AU  - Agarwala, Susama
AU  - Marcott, Cameron
TI  - Wilson loops in SYM $\mathcal{N}=4$ do not parametrize an orientable space
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2021
SP  - 583
EP  - 622
VL  - 8
IS  - 4
UR  - http://www.numdam.org/articles/10.4171/aihpd/111/
DO  - 10.4171/aihpd/111
LA  - en
ID  - AIHPD_2021__8_4_583_0
ER  - 
%0 Journal Article
%A Agarwala, Susama
%A Marcott, Cameron
%T Wilson loops in SYM $\mathcal{N}=4$ do not parametrize an orientable space
%J Annales de l’Institut Henri Poincaré D
%D 2021
%P 583-622
%V 8
%N 4
%U http://www.numdam.org/articles/10.4171/aihpd/111/
%R 10.4171/aihpd/111
%G en
%F AIHPD_2021__8_4_583_0
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://www.numdam.org/articles/10.4171/aihpd/111/

Cité par Sources :