In theoretical physics, one often considers gauge theory models whose symmetries are groups of large matrices, e.g. or . The limit of such theories for 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 . 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 whose square has a simialr role to Planck constant in semiclassical approximation limit of quantum mechanics.
A. A. Migdal, Loop equations and 1/N expansion, Physics Reports, 102 (4), 199-290 (1983) doi
Laurence G. Yaffe, Large N limits as classical mechanics, Rev. Mod. Phys. 54, 407–435 (1982) pdf
G ‘t Hooft, A planar diagram theory for strong interactions, Nuclear Physics B 72, 3 (1974), 461-473, doi