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

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

2010-05-08

arxiv.org/abs/1005.1350v1

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, 6 figures

Scientific paper

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.

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