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

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

2004-06-22

arxiv.org/abs/hep-th/0406191v3

JHEP0503:027,2005

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, 4 figures, LaTeX 2e, typos corrected, references added and a figure replaced

Scientific paper

10.1088/1126-6708/2005/03/027

We examine the two-dimensional U(N) Yang-Mills theory by using the technique of random partitions. We show that the large N limit of the partition function of the 2D Yang-Mills theory on S^2 reproduces the instanton counting of 4D N=2 supersymmetric gauge theories introduced by Nekrasov. We also discuss that we can take the ``double scaling limit'' by fixing the product of the N and cell size in Young diagrams, and the effective action given by Douglas and Kazakov is naturally obtained by taking this limit. We give an interpretation for our result from the view point of the superstring theory by considering a brane configuration that realizes 4D N=2 supersymmetric gauge theories.

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