Wilson loop correlators at strong coupling: from matrices to bubbling geometries

TL;DR

This paper calculates strong coupling correlators of supersymmetric Wilson loops with local operators in N=4 super Yang-Mills using matrix models and holography, confirming electric-magnetic duality through exact matches.

Contribution

It provides the first exact strong coupling computation of Wilson loop correlators using both matrix models and bubbling geometries, validating duality predictions.

Findings

Matrix model results match semiclassical 't Hooft loop calculations.

Holographic bubbling geometries reproduce gauge theory correlators.

Strong coupling correlators confirm electric-magnetic duality.

Abstract

We compute at strong coupling the large N correlation functions of supersymmetric Wilson loops in large representations of the gauge group with local operators of N=4 super Yang-Mills. The gauge theory computation of these correlators is performed using matrix model techniques. We show that the strong coupling correlator of the Wilson loop with the stress tensor computed using the matrix model exactly matches the semiclassical computation of the correlator of the 't Hooft loop with the stress tensor, providing a non-trivial quantitative test of electric-magnetic duality of N=4 super Yang-Mills. We then perform these calculations using the dual bulk gravitational picture, where the Wilson loop is described by a "bubbling" geometry. By applying holographic methods to these backgrounds we calculate the Wilson loop correlation functions, finding perfect agreement with our gauge theory results.