Quantum stabilization of the Belavin-Polyakov soliton

Using semiclassical techniques, we evaluate the quantum corrections to the mass of the soliton in the (2+1)-dimensional σ-model, assuming a coupling to a doublet of Dirac fermions. The fermionic determinant is calculated from several methods with complementary ranges of applicability. It tends to inflate the soliton. The mass correction from the boson loops turns out to be inversely proportional to the soliton size. We find that an essentially classical, stable soliton exists provided there are at least two species of fermions.