INDUCED FERMION NUMBER IN THE O(3) NONLINEAR SIGMA-MODEL

We study the fermion number induced by nontrivial topological configurations in the O(3) nonlinear model in 2+1 dimensions. We consider a scalar background configuration that adiabatically evolves from the normal vacuum to a soliton of winding number unity. The appearance of zero-energy modes is analyzed as a function of the relative magnitudes of the fermion mass scale mf and the inverse of the soliton width, 1s. We find a single energy-level crossing whenever mf>1s, implying that, as in the case of the O(4) model in four dimensions, the soliton carries the fermion number of any sufficiently heavy fermion. We also show the existence of states with fractional fermion number, QGS=12. © 1990 The American Physical Society.