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arXiv · hep-th/0005150

Hopf term induced by fermions

Alexander G. Abanov
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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.

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Alexander G. Abanov. 2000-07-31. Hopf term induced by fermions. https://doi.org/10.1016/s0370-2693(00)01118-7

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