PIRSA:25110052

New results on cohomological Hall algebras as line operators for HT theories

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}}
          }

Alexei Latyntsev University of Southern Denmark

Talk numberPIRSA:25110052
DOI10.48660/25110052
Collection
Talk Type Conference
Subject

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)