Large N limit of 2D Yang-Mills Theory and Instanton Counting

We examine the two-dimensional U(N) Yang-Mills theory by using the techniqueof random partitions. We show that the large N limit of the partition functionof the 2D Yang-Mills theory on S^2 reproduces the instanton counting of 4D N=2supersymmetric gauge theories introduced by Nekrasov. We also discuss that wecan take the ``double scaling limit'' by fixing the product of the N and cellsize in Young diagrams, and the effective action given by Douglas and Kazakovis naturally obtained by taking this limit. We give an interpretation for ourresult from the view point of the superstring theory by considering a braneconfiguration that realizes 4D N=2 supersymmetric gauge theories.Comment: 19 pages, 4 figures, LaTeX 2e, typos corrected, references added and a figure replace