Once extended unitary topological field theories

          @misc{ scivideos_PIRSA:24030093,
            doi = {10.48660/24030093},
            url = {https://pirsa.org/24030093},
            author = {Stehouwer, Luuk},
            keywords = {Quantum Matter},
            language = {en},
            title = {Once extended unitary topological field theories},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030093 see, \url{https://scivideos.org/index.php/pirsa/24030093}}
          }
          

Abstract

Motivated by the dagger category of Hilbert spaces, we explore the mathematical axiomatization of unitary topological field theory (TFT) using dagger categories. Recent advancements have elucidated the structure of higher dagger categories, paving the way for a precise definition of extended unitary TFTs. I will present an explicit formulation of once extended TFTs utilizing various versions of dagger bicategories. This framework enables a complete classification of unitary extended two-dimensional TFTs with arbitrary symmetry groups in terms of their unitary 2-representations. This is joint work in progress with Lukas Muller.