Functional renormalization group analysis of the O ( 3 ) nonlinear sigma model and non-Abelian bosonization duality
Junichi Haruna, Keito Shimizu, Masatoshi Yamada
It is known that the U ( 2 ) Wess-Zumino-Witten model is dual to the free fermion theory in two dimensions via non-Abelian bosonization. While it is decomposed into the S U ( 2 ) Wess-Zumino-Witten model and a free compact boson, the former is believed to be equivalent to the O ( 3 ) nonlinear sigma model with the theta term at θ = π . In this work, we reexamine this duality through the lens of nonperturbative 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 a 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.
arXiv:2405.14627•Physical review. D/Physical review. D.•Feb 18, 2025•1 citation