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The large N expansion of matrix-valued field theories was invented more than twenty years ago by ’t Hooft as a way to treat four-dimensional QCD with gauge group SU(N). At N = ∞ planar diagrams dominate and it was hoped that this fact would lead either to analytic results or to a reformulation of QCD as a string theory. While the original ideas remain attractive, the program has not yet been successful. It was slowly understood that N = ∞ field theories retain much of the complexity of the generic N case.

Advances in Large N Group Theory and the Solution of Two-Dimensional R 2 Gravity