Cohomological Hall algebras, vertex algebras and instantons
Rapcak, Miroslav ; Soibelman, Yan ; Yang, Yaping ; Zhao, Gufang
arXiv, 1810.10402 / Harvested from arXiv
Text on arXiv
We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of $\mathfrak{gl}(1)$. Based on that we derive the vertex algebra at the corner $\mathcal{W}_{r_1,r_2,r_3}$ of Gaiotto and Rapcak. We conjecture that our approach works for a big class of Calabi-Yau categories, including those associated with toric Calabi-Yau $3$-folds.
Publié le : 2018-10-24
Classification:  Mathematics - Quantum Algebra,  High Energy Physics - Theory,  Mathematics - Algebraic Geometry,  Mathematics - Representation Theory 
@article{1810.10402,
     author = {Rapcak, Miroslav and Soibelman, Yan and Yang, Yaping and Zhao, Gufang},
     title = {Cohomological Hall algebras, vertex algebras and instantons},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1810.10402}
}

Rapcak, Miroslav; Soibelman, Yan; Yang, Yaping; Zhao, Gufang. Cohomological Hall algebras, vertex algebras and instantons. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1810.10402/