Abstract
We derive an effective action for Dirac fermions coupled to O(3) non-linear σ-model (NL σM) through the Yukawa-type interaction. The nonperturbative (global) quantum anomaly of this model results in a Hopf term for the effective NL σM. We obtain this term using the “embedding” of the CP 1 model into the CP M 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 Chern–Simons term for an auxiliary gauge field.
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