The AdS/CFT correspondence has recently allowed the computation of gauge theory quantities in the strong coupled regime (for certain particular theories). One important such quantity is the Wilson loop which is related to the quark/ anti-quark potential, scattering amplitudes, etc. The computation is reduced to finding minimal area surfaces in hyperbolic space. Although this is a classical problem in mathematics its solution is not easy since it involves non-linear partial differential equations. In this talk I will describe some recent work where we found an infinite parameter family of such surfaces by using Riemann Theta functions to analytically solve the equations.

I am going to review, in the context of gauge theories, the anomalous dimension of twist two operators, the cusp anomaly of Wilson loops and how they relate through AdS/CFT to rotating strings in AdS space. Then I'm going to describe in more detail the spiky strings and their properties for large spin which allows us to obtain a relation between the anomalous dimension of twist two operators and the pp-wave anomaly, an anomaly we find when N=4 SYM theory is put in a pp-wave background. Finally I'm going to consider various new open string solutions describing Wilson loops in a pp-wave and in flat space. Based on 0802.2039 and 0804.3438.