Bosonization and anomalies of 3d fermionic topological orders

          @misc{ pirsa_PIRSA:24030079,
            doi = {10.48660/24030079},
            url = {https://pirsa.org/24030079},
            author = {Debray, Arun},
            keywords = {Condensed Matter},
            language = {en},
            title = {Bosonization and anomalies of 3d fermionic topological orders},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030079 see, \url{https://pirsa.org}}
          }
          

Abstract

here are two notions of a symmetry of a group G on a 3d topological order (TO): an "algebraic" symmetry, where G acts by automorphisms on the tensor category defining the (TO), and a "field-theoretic" symmetry, where the TFT corresponding to the TO is extended to manifolds with a principal G-bundle. The "field-theoretic" notion is stronger than the "algebraic" one, and the obstruction is sometimes referred to as the anomaly of the TO. The goal of this talk is to discuss a project joint with Weicheng Ye and Matthew Yu on computing these anomalies for fermionic TOs/spin TFTs: we develop a general framework employing Gaiotto-Kapustin's bosonic shadow construction. I will discuss both the mathematical conjectures our framework rests on as well as its use in examples. The Smith long exact sequence appears in our computations.