large N limit (Rev #1) in nLab

In theoretical physics, one often considers gauge theory models whose symmetries are groups of large matrices, e.g. U(N)U(N) or O(N)O(N). The limit of such theories for N→∞N\to \infty has often remarkable properties and string-like features.

This limit is sometimes appearing in its own right, but sometimes it is just considered as an approximation for a system with fixed finite NN. One of the features is that in the large N limit is that non-planar Feynman diagrams loose their importance and that the correlation functions satisfy certain decoupling/factorization rule. The behaviour is studied in terms of expansion in 1/N1/N whose square has a simialr role to Planck constant in semiclassical approximation limit of quantum mechanics.

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• G. ‘t Hooft, Large N, workshop lecture, hep-th/0204069
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• G.T. Horowitz, H. Ooguri, Spectrum of large N gauge theory from supergravity, hep-th/9802116.
• wikipedia 1/N expansion