Wilson loops: From 4D supersymmetric Yang-Mills theory to 2D Yang-Mills theory

In this paper we study supersymmetric Wilson loops restricted to an S-2 submanifold of four-dimensional space in N=4 super Yang-Mills theory. We provide evidence from both perturbation theory and the AdS dual that those loops are equal to the analogous observables in two-dimensional Yang-Mills on S-2 (excluding nonperturbative contributions). This relates a subsector of N=4 SYM to a low-dimensional soluble model and also suggests that this subsector of N=4 SYM is invariant under area preserving diffeomorphisms.