Minimal Area Surfaces, Riemann Theta Functions, and Integrability of Wilson Loops

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In this talk I will review recent results we obtained regarding the computation of Wilson loops in the context of the AdS/CFT correspondence. According to such correspondence Wilson loops are related to minimal area surfaces in hyperbolic space. The problem reduces to solving a set of non-linear but integrable differential equations. The solutions can be expressed in terms of Riemann theta functions. Other methods such as the dressing method applied to this problem will also be discussed.