PIRSA:25110067 Conference Mathematical physics

DOI10.48660/25110067

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

Dimofte, T. (2025). On the geometry of BPS algebras. Perimeter Institute. https://pirsa.org/25110067

Dimofte, Tudor. On the geometry of BPS algebras. Perimeter Institute, Nov. 07, 2025, https://pirsa.org/25110067 

@misc{ pirsa_PIRSA:25110067,
  doi = {10.48660/25110067},
  url = {https://pirsa.org/25110067},
  author = {Dimofte, Tudor},
  keywords = {Mathematical physics},
  language = {en},
  title = {On the geometry of BPS algebras},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {nov},
  note = {PIRSA:25110067 see, \url{https://pirsa.org}}
}

Abstract

I'll discuss the application of Tannakian methods to 4d holomorphic-topological QFT's, using boundary conditions and interfaces to represent the (braided meromorphic tensor) category of line operators. This leads to an explicit geometric construction of Yangian-like algebras, generalizing results of Costello-Yamazaki-Witten in 4d Chern-Simons. By applying these methods to twisted 4d N=2 theories, I'll explain how one recovers and extends some expected relations between cohomological Hall algebras of BPS states and line operators --- in particular, representing line operators as modules for "BPS Yangians."

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