We demonstrate that, in 1+1 dimensions, the effective action produced by massless fermions moving in external gravitational and gauge fields is identical with that produced by a suitably defined σ model which includes a Wess-Zumino term. This equivalence holds provided that the two models have the same conformal anomaly, a condition that we investigate in detail.
Brown, Lowell S.; Goldberg, Gary J.; Rim, Chaiho P.; and Nepomechie, Rafael I., "Non-Abelian Bosonization: Stress-Energy Correlation Functions" (1987). Physics Articles and Papers. 48.