Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories

Abstract

In this paper, we study irregular singular solution to Hitchin's equation and use it to describe four dimensional $N=2$ asymptotically free gauge theories. For $SU(2)$ $A$ type quiver, two kinds of irregular singularities besides one regular singularity are needed for the solution of Hitchin's equation; We then classify irregular singularities needed for the general $SU(N)$ $A$ type quiver.

37 pages, 6 figures

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• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Network, Cluster coordinates and N=2 theory I
• Network, cluster coordinates and N = 2 theory II: Irregular singularity
• The BPS Spectrum Generator In 2d-4d Systems