Mass generation in the large N-nonlinear σ-model

We study the infrared behaviour of the two-dimensional Euclidean O(N) nonlinear σ-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 [1].