Some aspects of the CP/sup N/-1 model

The CP/sup N/-1 models are analyzed by embedding them in a generalized two-parameter U(N) vector model. The model is solved in the large-N limit. This allows one to get a better understanding of how well large-N techniques extrapolate to finite N. In contrast to other models, the large-N limit in CP/sup N/-1 models is shown to be more singular. In a lattice version, a phase transition is shown to occur. Elitzur's theorem is also shown to be violated at N = infinity. Finally, the large-N limit does not reproduce an interesting property of finite-N CP/sup N/-1 theories. This concept, coined ''superconfinment,'' is defined and examined in detail both mathematically and physically. Why the large-N expansion fails to reproduce it is analyzed by making an analogy with a classical gas system