Wess-Zumino-Witten and fermion models in noncommutative space

We analyze the connection between Wess-Zumino-Witten and free fermion model s in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we deri ve the corresponding bosonization recipe studying, as an example, bosonizat ion of the U(N) Thirring model. Concerning the properties of the noncommuta tive Wess-Zumino-Witten model, we construct an orbit-preserving transformat ion that maps the standard commutative WZW action into the noncommutative o ne. (C) 2001 Elsevier Science B.V. All rights reserved.