Parafermionization, bosonization, and critical parafermionic theories

A bstract We formulate a ? k -parafermionization/bosonization scheme for one-dimensional lattice models and field theories on torus, starting from generalized Jordan-Wigner transformation lattice, which extends the Majorana-Ising duality at = 2. The -parafermionization enables us to investigate critical of parafermionic chains whose fundamental degrees freedom are parafermionic, we find that their criticality cannot be described by any existing conformal theory. modular transformations these low-energy as general consistency conditions found unconventional in partition functions torus transform differently theory when > Explicit forms obtained developed parafermionization large class -parafermionic chains, operator contents intrinsically distinct bosonic or fermionic model terms spins statistics. also use exhaust all minimal models, complementing earlier works cases.