Wenjun Niu, UC Davis

Abstract: Vertex algebras have been an important ingredients in the study of braided tensor category of line defects in 3d topological field theories. However, they are not the most convenient to work with, since the theory of intertwining operators is very complicated. In many cases, one has what is called a Kazhdan-Lusztig correspondence, which is an equivalence between braided tensor category of vertex algebra representations and quasi-triangular Hopf algebra representations, and the latter is significantly easier to work with. In this talk, I will introduce quantum supergroups associated to B twists of 3d N=4 abelian gauge theories, whose representation category is equivalent to the category of representations of the boundary vertex algebra as an abelian category. I will explain how the quantum supergroup representation category is braided and how we can upgrade the above equivalence into one of braided tensor categories. This is joint work in progress with T. Creutzig and T. Dimofte.