The θ = π nonlinear sigma model is massless

Abstract

We consider here the O(3) nonlinear sigma model in 1 + 1 dimensions with the topological parameter θ = π, which is of considerable interest in quantum field theory as well as the study of chains of half-integral spin. We first define a lattice regulated version of the model and show that it is massless for all values of the coupling g and that it is governed by the k = 1 Wess-zumino-Witten (WZW) fixed point.