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

TL;DR

This paper explores irregular singular solutions to Hitchin's equation to model four-dimensional $N=2$ asymptotically free gauge theories, classifying the necessary singularities for various gauge groups.

Contribution

It introduces a classification of irregular singularities in Hitchin's equations relevant to $N=2$ gauge theories, extending understanding beyond regular singularities.

Findings

Irregular singular solutions describe $N=2$ asymptotically free theories.

Two types of irregular singularities are needed for $SU(2)$ quivers.

Classification of irregular singularities for $SU(N)$ quivers is provided.

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.