ZN duality and parafermions revisited

Given a two-dimensional bosonic theory with a non-anomalous Z(2) symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF theory with level 2. From a Hamiltonian perspective, the information of dualities is encoded in a topological boundary state which is defined as an eigenstate of certain Wilson loop operators (anyons) in the bulk. We generalize this story to two-dimensional theories with non-anomalous Z(N) symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with Z(N) or subgroups of Z(N), and discuss their algebraic properties as well as the Z(N) duality web.