Mass Generation in the Large N nonlinear sigma-Model

Details Mass Generation in the Large N nonlinear sigma-Model Mass Generation in the Large N nonlinear sigma-Model

1999-02-16

arxiv.org/abs/math-ph/9902020v1

Commun.Math.Phys. 202 (1999) 89-126

Physics

Mathematical Physics

44 pages

Scientific paper

10.1007/s002200050576

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.

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