Categories of line defects and cohomological Hall algebrasConfirmed

by Nikita Grygoryev (Perimeter Institute / University of Waterloo)

Thursday Sep 12, 2024, 11:00 a.m. → 12:30 p.m. America/Toronto

PI/4-400 - Space Room (Perimeter Institute for Theoretical Physics)

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.