Gapped Phases with Non-Invertible Symmetries: (1+1)d

Understand

We propose a general framework to characterize gapped infra-red (IR) phases of theories with non-invertible (or categorical) symmetries.

• In this paper we focus on (1+1)d gapped phases with fusion category symmetries.
• The approach that we propose uses the Symmetry Topological Field Theory (SymTFT) as a key input: associated to a field theory in d spacetime dimensions, the SymTFT lives in one dimension higher and admits a gapped boundary, which realizes the categorical symmetries.
• It also admits a second, physical, boundary, which is generically not gapped.