# Categories of line defects and cohomological Hall algebras

### APA

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

### MLA

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

### BibTex

@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}} }

**Collection**

**Subject**

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.