Unsuppressed fermion-number violation at high temperature: An O(3) model.

Abstract

The O(3) nonlinear \ensuremath{\sigma} model in 1+1 dimensions, modified by an explicit symmetry-breaking term, is presented as a model for baryon- and lepton-number violation in the standard electroweak theory. Although arguments based on the Atiyah-Singer index theorem and instanton physics apply to the model, we show by explicit calculations that the rate of chiral fermion-number violation due to the axial anomaly is entirely unsuppressed at sufficiently high temperatures. Our results apply to unbroken gauge theories as well and may require reevaluation of the role of instantons in high-temperature QCD.