Critical O(N) - vector nonlinear sigma - models: A resume of their field structure

Abstract

The classification of quasi - primary fields is outlined. It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N) - Noether currents. Derivation of all quasi - primary fields and the resolution of degeneracy is sketched. Finally the limits d=2 and d=4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so.

16 pages, Latex. To appear in the Proceedings of the XXII Conference on Differential Methods in Theoretical Physics, Ixtapa, Mexico, September 20-24, 1993

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