Correlators of Hopf Wilson loops in the AdS/CFT correspondence

Abstract

We study at quantum level correlators of supersymmetric Wilson loops with contours lying on Hopf fibers of ${S}^{3}$. In $\mathcal{N}=4$ super Yang-Mills theory the strong coupling analysis can be performed using the AdS/CFT correspondence and a connected classical string surface, linking two different fibers, is presented. More precisely, the string solution describes oppositely oriented fibers with the same scalar coupling and depends on an angular parameter, interpolating between a nonsupersymmetric configuration and a supersymmetric one. The system can be thought as an alternative deformation of the ordinary antiparallel lines giving the static quark-antiquark potential, that is indeed correctly reproduced, at weak and strong coupling, as the fibers approach one another.