Anomalies and the Large N Limit

Operator algebra aspects of the Large N limit of Bosonic vector models are analyzed. It is shown that the Large N limit is a classical theory, and a general method, based on defromation quatization, for calculating the Poisson algebra of dynamical observables in the limiting classical theory is presented. The Poisson algebra of O(N) invariant observables of Bosonic vector models is constructed in this approach, and is shown to be a central extension of the Symplectic Lie algebra. The relation of the central term to anomalies is discussed. A comparision of the classical theories obtained in the Large N limit and that in the small (ℎ/2π) limit is also presented