ONE-LOOP EFFECTIVE ACTION IN THE SIGMA-MODEL FOR A PERIODIC-CHIRAL-FIELD ANSATZ

One-fermion and one-boson loop contributions to the effective action in the Gell-Mann-Lévy f model are calculated analytically for the case of a periodic-chiral-field ansatz. Accuracy and limits of validity of various approximate methods used in the effective-action formalism are tested quantitatively on this example, in particular, the convergence of the gradient expansion. Vacuum instability of the theory at the one-loop level is found, in agreement with earlier results for solitons. © 1990 The American Physical Society.