In this seminar, I will discuss some recent results regarding two different Wilson loop operators in N=4 super Yang-Mills theory: (i) a cusped line for particles in large symmetric representations of the gauge group and (ii) the so-called 1/4 BPS latitude on a two-sphere. In the former case, I will outline a conjecture claiming that, in a particular limit, an eikonal exponentiation takes place, with the full non-perturbative result for the Wilson line expectation value being captured by the exponential of the 1-loop result. This can be checked holographically via a D-brane computation and opens up a new window into the strong coupling behavior of operators which are not protected by supersymmetry. In the latter case of the supersymmetric latitude, I will report on a recent attempt to match a strong coupling gauge theory prediction obtained via localization with the computation of the 1-loop determinant of the string fluctuations around the dual classical surface in AdS. The predicted result is captured by some special modes of the string fluctuations, hinting at the possibility of some localization mechanism in string theory.
