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.
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Lowell S. Brown, and Rafael I. Nepomechie, Physical Review D, 35, 3239-3248, 1987. "Copyright © 1987 by the American Physical Society.”
Link to the online abstract: http://link.aps.org/doi/10.1103/PhysRevD.35.3239
DOI: 10.1103/PhysRevD.35.3239