QM Research Seminar: Towards all Categorical Symmetries in 2+1 Dimensions

Recent studies on symmetries are often focused on those non-invertible symmetries that steer away from familiar (invertible) group-like structures, but in recent works (2408.13931) by M. Bullimore and myself, we conjecture that in fact all finite symmetries of oriented 3-dimensional QFTs can be constructed by employing tools from group theory. In the first half of this talk we will review category-theoretic descriptions of non-invertible symmetries and how this data is closely related to that of higher-dimensional (symmetry) TFTs. In the latter half of the talk we will shift our focus to symmetries in 3d, aiming to demonstrate a classification in terms of the category of gapped/topological boundary conditions of 4-dimensional Dijkgraaf-Witten theory.