Semiclassical spectrum of the two-dimensional non-linear sigma models

The spectrum of O(N) invariant two-dimensional non-linear sigma models is analyzed for large N by the methods of Dashen, Hasslacher and Neveu. Calculations to O(1/N) are carried out and the spectrum is shown to consist solely of N degenerate massive mesons. This is consistent with strong coupling lattice calculations and indicates that for sufficiently large N there is no phase transition between the weak and strong coupling regions. (Auth.)