Integrability of smooth Wilson loops in $ \mathcal{N}=4 $ superspace

We perform a detailed study of the Yangian symmetry of smooth supersym- metric Maldacena-Wilson loops in planar N = 4 super Yang-Mills theory. This hidden symmetry extends the global superconformal symmetry present for these observables. A gauge-covariant action of the Yangian generators on the Wilson line is established that generalizes previous constructions built upon path variations. Employing these generators the Yangian symmetry is proven for general paths in non-chiralN = 4 superspace at the rst perturbative order. The bi-local piece of the level-one generators requires the use of a regulator due to divergences in the coincidence limit. We perform regularization by point splitting in detail, thereby constructing additional local and boundary contributions as regularization for all level-one Yangian generators. Moreover, the Yangian algebra at level one is checked and compatibility with local kappa-symmetry is established. Finally, the consistency of the Yangian symmetry is shown to depend on two properties: the vanishing of the dual Coxeter number of the underlying superconformal algebra and the existence of a novel superspace \G-identity" for the gauge eld theory. This tightly constrains the conformal gauge theories to which integrability can possibly apply.