Correlators of Hopf Wilson loops in the AdS/CFT correspondence

TL;DR

This paper investigates quantum correlators of supersymmetric Wilson loops on Hopf fibers in $ ext{S}^3$, using AdS/CFT to analyze classical string surfaces connecting different fibers and exploring their BPS properties.

Contribution

It introduces a new classical string solution in AdS/CFT for Wilson loops on Hopf fibers, interpolating between BPS and non-BPS configurations, and relates it to quark-antiquark potential.

Findings

String solutions describe fibers with opposite orientations and same scalar coupling.

The system interpolates between BPS and non-BPS states via an angular parameter.

The potential matches weak and strong coupling results as fibers approach each other.

Abstract

We study at quantum level correlators of supersymmetric Wilson loops with contours lying on Hopf fibers of $S^3$. In $\mathcal{N}=4$ SYM 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 non-BPS configuration and a BPS 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.