Geometrical phases and quantum numbers of solitons in nonlinear sigma-models

Abstract

Solitons of a nonlinear field interacting with fermions often acquire a fermionic number or an electric charge if fermions carry a charge. We show how the same mechanism (chiral anomaly) gives solitons statistical and rotational properties of fermions. These properties are encoded in a geometrical phase, i.e., an imaginary part of a Euclidian action for a nonlinear sigma-model. In the most interesting cases the geometrical phase is non-perturbative and has a form of an integer-valued theta-term.

5 pages, no figures

References in corpus (2)

• Theta-terms in nonlinear sigma-models
• Chiral non-linear sigma-models as models for topological superconductivity

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