We discuss bosonization in three dimensions by establishing a connection between the massive Thirring model and the MaxwellChern-Simons theory. We show, to lowest order in inverse fermion mass, the identity between the corresponding partition functions; from this, a bosonization identity for the fermion current, valid for length scales long compared with the Compton wavelength of the fermion, is inferred. We present a non-local operator in the Thirring model which exhibits fractional statistics. * Investigador CICBA, Argentina

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We discuss bosonization in three dimensions of an SU (N ) massive Thirring model in the low-energy regime. We find that the bosonized theory is related (but not equal) to SU (N ) Yang-Mills-Chern-Simons gauge theory. For free massive fermions bosonization leads, at low energies, to the pure SU (N ) (level k = 1) Chern-Simons theory.

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We compute the exact canonically induced parity breaking part of the effective action for 2+1 massive fermions in particular Abelian and non Abelian gauge field backgrounds. The method of computation resorts to the chiral anomaly of the dimensionally reduced theory.

We obtain the contributions to the renormalization group functions of all the diagrams containing the unique one-loop primitive divergence of a simple supersymmetric Wess-Zumino model, up to more than 200 loops. The asymptotic behavior of the coefficients in the expansion of the anomalous dimension is analysed. * On leave from, Laboratoire de Physique Théorique et Hautes Energies, Boite 126, 4 Place Jussieu, 75252 Paris Cedex 05.