We demonstrate that, in 1+1 dimensions, the effective action produced by massless fermions moving in external gauge potentials is identical with that produced by a suitably defined σ model which includes a Wess-Zumino term. Hence the current correlation functions of the fermion and boson theories are identical.
Brown, Lowell S. and Nepomechie, Rafael I., "Non-Abelian Bosonization: Current Correlation Functions" (1987). Physics Articles and Papers. 44.