# Cohomological Hall Algebras, Vertex Algebras and Instantons

@article{Rapk2020CohomologicalHA,
title={Cohomological Hall Algebras, Vertex Algebras and Instantons},
author={Miroslav Rap{\vc}{\'a}k and Y. Soibelman and Yaping Yang and G. Zhao},
journal={Communications in Mathematical Physics},
year={2020},
volume={376},
pages={1803-1873}
}
• Miroslav Rapčák, +1 author G. Zhao
• Published 2020
• Physics, Mathematics
• Communications in Mathematical Physics
• 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 $$\mathfrak {gl}(1)$$ gl ( 1 ) . Based on that we derive the vertex algebra at the corner $${\mathcal {W}}_{r_{1},r_{2},r_{3}}$$ W r 1 , r 2 , r 3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those… CONTINUE READING
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