  Planarity was introduced by 't Hooft in his topological classification of
diagrams in the large-N limit of U(N) gauge theories. Planarity also occurs in
noncommutative field theories where amplitudes possess invariance only under
cyclic permutations, a feature inherited from the parent string theory. In
noncommutative gauge theories both kinds of planarity merge in a context which
turns out to be particularly intriguing in the two-dimensional case where gauge
invariant correlators can be explicitly computed.
