SymTFT actions, Condensable algebras and Categorical anomaly resolutions

We investigate symmetry topological field theories (SymTFTs) of non-abelian and non-invertible symmetries and the different Lagrangian algebras associated with a given Drinfeld center. For several examples we analyze the condensable algebras of the Drinfeld center to identify the intrinsically gapless symmetry protected topological (igSPT) phases. In previous work, the relation between igSPT phases and resolving anomalies by embedding an anomalous symmetry inside a larger fusion category was demonstrated. Here we present more examples of this mechanism that involve both group-like and categorical symmetries.