PIRSA:25110065 Conference Mathematical physics

DOI10.48660/25110065

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

Grygoryev, N. (2025). BPS lines, CoHA bimodules and Cluster Categorification. Perimeter Institute. https://pirsa.org/25110065

Grygoryev, Nikita. BPS lines, CoHA bimodules and Cluster Categorification. Perimeter Institute, Nov. 06, 2025, https://pirsa.org/25110065 

@misc{ pirsa_PIRSA:25110065,
  doi = {10.48660/25110065},
  url = {https://pirsa.org/25110065},
  author = {Grygoryev, Nikita},
  keywords = {Mathematical physics},
  language = {en},
  title = {BPS lines, CoHA bimodules and Cluster Categorification},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {nov},
  note = {PIRSA:25110065 see, \url{https://pirsa.org}}
}

Abstract

In four-dimensional N=2 supersymmetric quantum field theories, half-BPS line defects survive the HT twist and are expected to form a monoidal category equipped with renormalized r-matrices. The Grothendieck group of this category is anticipated to coincide with the cluster algebra associated to the BPS quiver Q. Starting from such a quiver, we propose a candidate for such a category - roughly speaking, to each possible framing we associate a bimodule over the Cohomological Hall algebra of Q, and consider the subcategory they generate. We conjecture that this construction satisfies the expected properties. In this talk, I will present examples where this approach works and explain why we expect the RG functors to play the role of "categorified quantum torus charts".

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