IAS CMP/QFT Group Meeting

Abstract: Fusion 2-categories offer a higher dimensional generalization of the category of symmetries in (1+1)d. I will explain how to leverage fusion 2-categories in a special case and apply them to understand the categorical structure of (3+1)d and (4+1)d fermionic TQFTs. In particular, the TQFTs in these dimensions can be classified, up to gapped boundary conditions using fusion 2-categories. The recent classification of fusion 2-categories allows us to extend our understanding to TQFTs with G-anomalies, which is important for the problem of anomaly matching with some UV theory. I will explain how such TQFTs are constructed as well as the mathematical structure of these theories.