Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-05-16
Phys.Lett. B492 (2000) 321-323
Physics
High Energy Physics
High Energy Physics - Theory
5 pages, no figures, latex, elsart.cls, minor errors are corrected
Scientific paper
10.1016/S0370-2693(00)01118-7
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.
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