Abstract

Two-dimensional (2d) topological phases are characterized by a unitary modular tensor category(UMTC) along with the chiral central charge c_. For non-chiral topological phases, where c.vanishes, the topological phase is fully described by a UMTC. There are two prominent classes oflattice models that realize 2d non-chiral topological phases: (i) Kitaevs quantum double models and(il) Levin and Wens string-net models. These two model classes are intimately related. This talk wilpresent a generalization of Kitaevs quantum double models to weak Hopf algebras, as well as ageneralization of Levin-Wen string-net models to multifusion categories. We wil establish aneguivalence between these two broader classes of lattice models for non-chiral 2D topologicalphases. From the perspective of lattice gauge theory, we introduce weak Hopf gauge and chargesymmetries. In particular, we elucidate the weak Hopf symmetry underlying the multifusion stringnet models.Some interesting open problems related to these generalizations will also behighlighted.