PIRSA:25110052 Conference Mathematical physics

DOI10.48660/25110052

Conference/School: Holomorphic-topological field theories and representation theory

Latyntsev, A. (2025). New results on cohomological Hall algebras as line operators for HT theories. Perimeter Institute. https://pirsa.org/25110052

Latyntsev, Alexei. New results on cohomological Hall algebras as line operators for HT theories. Perimeter Institute, Nov. 03, 2025, https://pirsa.org/25110052 

@misc{ pirsa_PIRSA:25110052,
  doi = {10.48660/25110052},
  url = {https://pirsa.org/25110052},
  author = {Latyntsev, Alexei},
  keywords = {Mathematical physics},
  language = {en},
  title = {New results on cohomological Hall algebras as line operators for HT theories},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {nov},
  note = {PIRSA:25110052 see, \url{https://pirsa.org}}
}

Abstract

We discuss a sequence of projects (some in progress) constructing "line operator categories for 4d HT theories" from CY3 manifolds and categories. Concretely - in certain settings, the CY3 cohomological Hall algebra B (due to Kontsevich--Soibelman any many others) we show admits a Drinfeld-style vertex coproduct coloured by the cohomology of the CY3. We explain how to apply Majid vertex bosonisation to this structure to get a category B-Mod(H-Mod) factorising over the complex line C. This involves proving that B is a "vertex quantum group". Examples include quivers with potential - where we compare to Drinfeld/Yang-Zhao/Davison coproducts - canonical bundles of CY2s, deformed CY3 completions (and by work in progress - a larger class of examples). Joint with Šarūnas Kaubrys, Shivang Jidnal, (and Pierre Descombes)

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