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.
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Lowell S. Brown, Gary J. Goldberg, Chaiho P. Rim and Rafael I. Nepomechie, Physical Review D, 36, 551-561, 1987. "Copyright © 1987 by the American Physical Society.”
Link to the online abstract: http://link.aps.org/doi/10.1103/PhysRevD.36.551
DOI: 10.1103/PhysRevD.36.551