Theta-terms in nonlinear sigma-models

We trace the origin of theta-terms in nonlinear sigma-models as a nonperturbative anomaly of current algebras. The nonlinear sigma-models emerge as a low energy limit of fermionic sigma-models. The latter describe Dirac fermions coupled to chiral bosonic fields. We discuss the geometric phases in three hierarchies of fermionic sigma-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 theta-terms. We emphasize a relation between B-terms and quantum numbers of solitons, (C) 2000 Elsevier Science B.V. All rights reserved.