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

Abstract

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.

arXiv comment19 pages, 4 figures, LaTeX 2e, typos corrected, references added and a figure replaced

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Cited by in corpus (9)

• Chern-Simons Theory, 2d Yang-Mills, and Lie Algebra Wanderers
• Chern-Simons Theory in Lens Spaces from 2d Yang-Mills on the Cylinder
• Instanton Counting and Matrix Model
• Localization on the D-brane, two-dimensional gauge theory and matrix models
• Instanton Counting and Dielectric Branes
• Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective
• Dimensional Reduction of Seiberg-Witten Monopole Equations, N=2 Noncommutative Supersymmetric Field Theories and Young Diagrams
• Instantons, Fluxons and Open Gauge String Theory
• Whittaker vectors at finite energy scale, topological recursion and Hurwitz numbers