Higher S-matrices and higher modular categories

          @misc{ pirsa_PIRSA:22060017,
            doi = {10.48660/22060017},
            url = {https://pirsa.org/22060017},
            author = {Reutter, David},
            keywords = {Mathematical physics},
            language = {en},
            title = {Higher S-matrices and higher modular categories},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060017 see, \url{https://pirsa.org}}
          }
          

Abstract

"Every braided fusion category has a `framed S-matrix pairing' which records the braiding between simple objects. Non-degeneracy/Morita invertibility of the category (aka `modularity' in the oriented case) is equivalent to non-degeneracy of this pairing. I will define higher-dimensional versions of S-matrices which pair morphisms of complementary dimension in higher semisimple categories and sketch a proof that these pairings are non-degenerate if and only if the higher category is. Along the way, I will introduce higher semisimple categories and higher fusion categories and interpret these results in terms of the associated anomalous topological quantum field theories. This is based on joint work in progress with Theo Johnson-Freyd."