Categorical Aspects of Symmetry in Fermionic Systems

          @misc{ scivideos_PIRSA:24030089,
            doi = {10.48660/24030089},
            url = {https://pirsa.org/24030089},
            author = {Ohmori, Kantaro},
            keywords = {Quantum Matter},
            language = {en},
            title = {Categorical Aspects of Symmetry in Fermionic Systems},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030089 see, \url{https://scivideos.org/pirsa/24030089}}
          }
          

Abstract

In this talk we explore the symmetry in 1+1d fermionic systems from a category theory perspective. We argue that It requires additional structure than a tensor category over sVect, and rather captured by a fusion category equipped with a braided central functor from a specific braided fusion category, dependent on the chiral central charge. The same data defines a 1-morphism in the 4-category of braided tensor categories, which lead us to a 4d-3d-2d picture via cobordism hypothesis. This talk is based on an ongoing work with K. Inamura.