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The master field on the plane

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I will discuss the large N limit of the pure Yang-Mills theory on the Euclidean plane with structure group U(N). One of the nice features of this limit is the emergence of the Makeenko-Migdal equations, which were originally derived by an integration by parts in an ill-defined functional integral, and which can be rigorously understood in terms of the combinatorics of large rotationally invariant random unitary matrices.

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