Mass Generation in the Large N nonlinear sigma-Model

TL;DR

This paper proves that the two-dimensional Euclidean O(N) nonlinear sigma-Model becomes massive with exponential decay of correlations for large but finite N, using a bosonic field representation that preserves symmetry.

Contribution

It introduces a simplified proof that the model is massive at large N without breaking O(N)-symmetry, improving on previous methods.

Findings

Model is massive for sufficiently large N

Correlation functions decay exponentially

Proof avoids symmetry breaking

Abstract

We study the infrared behaviour of the two-dimensional Euclidean O(N) nonlinear sigma-Model with a suitable ultraviolet cutoff. It is proven that for a sufficiently large (but finite!) number N of field components the model is massive and thus has exponentially decaying correlation functions. We use a representation of the model with an interpolating bosonic field. This permits to analyse the infrared behaviour without any intermediate breaking of O(N)-symmetry. The proof is simpler than that of the corresponding result for the Gross-Neveu-Model.