Select All
PIRSA:22060017

Video URL

https://pirsa.org/22060017

Higher S-matrices and higher modular categories

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060017 see, \url{https://scivideos.org/pirsa/22060017}}
          }

David Reutter Universität Hamburg

Talk numberPIRSA:22060017
DOI10.48660/22060017
Source RepositoryPIRSA
Collection
Talk Type Conference
Subject

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."