Anomaly resolution by non-invertible symmetries

In this paper we generalize previous results on anomaly resolution to noninvertible symmetries. Briefly, given a global symmetry G of some theory with a 't Hooft anomaly rendering it ungaugeable, the idea of anomaly resolution is to extend G to a larger anomaly-free symmetry of the same theory with a trivially-acting kernel. In previous work, several of the coauthors demonstrated that in two-dimensional theories, by virtue of decomposition, gauging the larger symmetry is equivalent to a disjoint union of theories in which a nonanomalous subgroup of G is gauged. In this paper, we consider examples in which the larger symmetry is not a group, but instead a noninvertible symmetry defined by some fusion category. In principle the same ideas apply to the case that G itself is noninvertible. We discuss the construction of larger symmetries using both SymTFT methods as well as algebraically via (quasi-)Hopf algebras.