Journal article

Cohomological Hall Algebras, Vertex Algebras and Instantons

Miroslav Rapcak, Yan Soibelman, Yaping Yang, Gufang Zhao

Communications in Mathematical Physics | SPRINGER | Published : 2020

Abstract

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 gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds.