Functional Renormalization Group Analysis of O (3) Nonlinear Sigma Model and Non-Abelian Bosonization Duality

It is known that the SU (2) Wess-Zumino-Witten model is dual to the free fermion theory in two dimensions via non-Abelian bosonization. Additionally, the SU (2) Wess-Zumino-Witten model is believed to be equivalent to the O (3) nonlinear sigma model with the theta term. In this work, we reexamine this duality through the lens of renormalization group (RG) flow. We analyze the RG flow structure of the O (3) nonlinear sigma model with the theta term in two dimensions using the functional renormalization group. Our results reveal a nontrivial fixed point with a nonzero value of the topological coupling. The scaling dimensions (critical exponents) at this fixed point suggest the realization of duality between the O (3) nonlinear sigma model with the theta term and the free fermion theory, indicating that these models belong to the same universality class.