QUANTUM MECHANICALLY INDUCED WESS–ZUMINO TERM IN THE PRINCIPAL CHIRAL MODEL

Abstract

It is argued that in the two-dimensional principal chiral model, the Wess–Zumino term may be induced quantum mechanically in a manner analogous to the θ-term in QCD. Our argument is based on the fact that the configuration space of the model has a structure topologically identified as a sphere, and that the Dirac monopole potential, which is induced on the sphere by inequivalent quantizations, appears in the guise of the Wess–Zumino term. Our result suggests that, at the critical value λ2=8π/|k| of the coupling constant, the principal chiral model belongs to the same family of models with the Wess–Zumino–Novikov–Witten model at the quantum level.