IAS Informal Physics Seminar
Symmetry Topological Field Theory for 1+1d Lattice Models and 2+1d Gapped Phases with Categorical Symmetries
Abstract: Non-invertible categorical symmetries have emerged as a powerful tool to uncover new beyond-Landau quantum phases and phase transitions. The general theory of such phases and transitions has been studied systematically primarily in (1+1)d using the framework of the Symmetry Topological Field Theory (SymTFT), also known as Topological Holography. In this talk, I will describe two complimentary directions based on the SymTFT framework. Firstly I will describe how the SymTFT information can be converted into lattice chains realizing phases and transitions with categorical symmetries. Secondly, I will use the SymTFT to study and classify gapped phases in (2+1)d for a class of categorical symmetries, referred to as bosonic type, the SymTFT for which are finite group (3+1)d Dijkgraaf-Witten theories.
Based on: https://arxiv.org/abs/2405.05964 and https://arxiv.org/abs/2408.05266