Exact form factors of the O(N) σ-model

Abstract

A general form factor formula for the O(N) σ-model is constructed and applied to several operators. The large N limits of these form factors are computed and compared with the 1/N expansion of the O(N) σ-model in terms of Feynman graphs and full agreement is found. In particular, O(3) and O(4) form factors are discussed. For the O(3) σ-model several low particle form factors are calculated explicitly.