Hopf term induced by fermions

We derive an effective action for Dirac fermions coupled to O(3) non-linear sigma -model (NL sigmaM) through the Yukawa-type interaction. The nonperturbative (global) quantum anomaly of this model results in a Hopf term for the effective NL sigmaM. We obtain this term using the "embedding" of the CP1 model into the CPM generalization of the model which makes the quantum anomaly perturbative. This perturbative anomaly is calculated by means of a gradient expansion of a fermionic determinant and is given by the Chem-Simons term for an auxiliary gauge field. (C) 2000 Elsevier Science B.V. All rights reserved.