  We argue that Hitchin's equation determines not only the low energy effective
theory but also describes the UV theory of four dimensional N=2 superconformal
field theories when we compactify six dimensional $A_N$ $(0,2)$ theory on a
punctured Riemann surface. We study the singular solution to Hitchin's equation
and the Higgs field of solutions has a simple pole at the punctures; We show
that the massless theory is associated with Higgs field whose residual is a
nilpotent element; We identify the flavor symmetry associated with the puncture
by studying the singularity of closure of the moduli space of solutions with
the appropriate boundary conditions. For the mass-deformed theory the residual
of the Higgs field is a semi-simple element, we identify the semi-simple
element by arguing that the moduli space of solutions of mass-deformed theory
must be a deformation of the closure of the moduli space of the massless
theory. We also study the Seiberg-Witten curve by identifying it as the
spectral curve of the Hitchin's system. The results are all in agreement with
Gaiotto's results derived from studying the Seiberg-Witten curve of four
dimensional quiver gauge theory.
