Theta-terms in nonlinear sigma-models Original Research Article

We trace the origin of θ-terms in nonlinear σ-models as a nonperturbative anomaly of current algebras. The nonlinear σ-models emerge as a low energy limit of fermionic σ-models. The latter describe Dirac fermions coupled to chiral bosonic fields. We discuss the geometric phases in three hierarchies of fermionic σ-models in space-time dimension (d+1) with chiral bosonic fields taking values on d-, d+1-, and d+2-dimensional spheres. The geometric phases in the first two hierarchies are θ-terms. We emphasize a relation between θ-terms and quantum numbers of solitons.