BPS lines, CoHA bimodules and Cluster Categorification

          @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".