Categorical Landau Paradigm for Gapped Phases

We propose a unified framework to classify gapped infrared phases with categorical symmetries, leading to a generalized, categorical Landau paradigm. This is applicable in any dimension and gives a succinct, comprehensive, and computationally powerful approach to classifying gapped symmetric phases. The key tool is the symmetry topological field theory, which is a one dimension higher topological field theory with two boundaries that we choose to be topological. We illustrate the general idea for (1+1)D gapped phases with categorical symmetries and suggest higher-dimensional extensions.