Cohomological Hall algebras, vertex algebras and instantons

M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical Physics (2019).


Journal Article | Epub ahead of print | English
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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.
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2019-09-21
Journal Title
Communications in Mathematical Physics
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Cite this

Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 2019. doi:10.1007/s00220-019-03575-5
Rapcak, M., Soibelman, Y., Yang, Y., & Zhao, G. (2019). Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. https://doi.org/10.1007/s00220-019-03575-5
Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical Physics, 2019. https://doi.org/10.1007/s00220-019-03575-5.
M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras, vertex algebras and instantons,” Communications in Mathematical Physics, 2019.
Rapcak M, Soibelman Y, Yang Y, Zhao G. 2019. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics.
Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” Communications in Mathematical Physics, Springer Nature, 2019, doi:10.1007/s00220-019-03575-5.

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