ℤN duality and parafermions revisited

A bstract 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.