PIRSA:24090162 Scientific Series Mathematical physics

DOI10.48660/24090162

Series: Mathematical Physics

Grygoryev, N. (2024). Categories of line defects and cohomological Hall algebras. Perimeter Institute. https://pirsa.org/24090162

Grygoryev, Nikita. Categories of line defects and cohomological Hall algebras. Perimeter Institute, Sep. 12, 2024, https://pirsa.org/24090162 

@misc{ pirsa_PIRSA:24090162,
  doi = {10.48660/24090162},
  url = {https://pirsa.org/24090162},
  author = {Grygoryev, Nikita},
  keywords = {Mathematical physics},
  language = {en},
  title = {Categories of line defects and cohomological Hall algebras},
  publisher = {Perimeter Institute},
  year = {2024},
  month = {sep},
  note = {PIRSA:24090162 see, \url{https://pirsa.org}}
}

Abstract

BPS line defects in 4d N=2 supersymmetric QFT are described by a monoidal category with a list of desired properties. For example, the Grothendieck group of this category is supposed to coincide with quantization of functions on Coulomb branch of the theory compactified on a circle. Based on an observation, that at a given vacuum the spectrum of PBS particles can be quipped with an algebra structure – cohomological Hall algebra of the corresponding BPS quiver – we propose a category generated by certain bimodules over this algebra that possesses expected properties of the category of lines. Based on a joint work with Davide Gaiotto and Wei Li. 

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