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

Abstract

In this paper we study supersymmetric Wilson loops restricted to an ${S}^{2}$ submanifold of four-dimensional space in $\mathcal{N}=4$ 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 $\mathcal{N}=4$ SYM to a low-dimensional soluble model and also suggests that this subsector of $\mathcal{N}=4$ SYM is invariant under area preserving diffeomorphisms.