Hopf term induced by fermions

Abstract

We derive an effective action for Dirac fermions coupled to O(3) non-linear sigma-model (NLSM) through the Yukawa-type interaction. The nonperturbative (global) quantum anomaly of this model results in a Hopf term for the effective NLSM. 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.

5 pages, no figures, latex, elsart.cls, minor errors are corrected

References in corpus (1)

• Theta-terms in nonlinear sigma-models

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