Multi-instanton valleys in the O(3) sigma model.

Abstract

An explicit construction is given for valleys in the configuration space of an arbitrary number of instanton-anti-instanton pairs for the O(3) nonlinear $\ensuremath{\sigma}$ model in two dimensions. The $\ensuremath{\sigma}$-model action is supplemented by an explicit conformal-symmetry-breaking term and the multi-instanton valleys are used to examine the relative importance of single- and multi-instanton contributions to anomalous scattering. Numerical solutions to the saddle-point equations for the cross section are presented which support the existence of a critical energy above which the dilute instanton gas approximation breaks down. The relevance of these results to the problem of multi-instanton corrections to processes which violate baryon number in the standard model is discussed.