Correlators of supersymmetric Wilson loops at weak and strong coupling

TL;DR

This paper investigates the correlators of BPS Wilson loops in N=4 supersymmetric Yang-Mills theory, confirming weak coupling predictions via localization and exploring strong coupling behavior through supergravity, revealing partial agreement.

Contribution

It provides explicit weak coupling calculations matching localization results and analyzes strong coupling correlators using supergravity, highlighting discrepancies in coefficients.

Findings

Weak coupling results agree with localization predictions within 10^(-4)

Strong coupling supergravity reproduces geometric dependence but not the exact coefficient

Validation of BPS Wilson loop correlators across coupling regimes

Abstract

We continue our study of the correlators of a recently discovered family of BPS Wilson loops in N=4 supersymmetric U(N) Yang-Mills theory. We perform explicit computations at weak coupling by means of analytical and numerical methods finding agreement with the exact formula derived from localization. In particular we check the localization prediction at order g^6 for different BPS "latitude" configurations, the N=4 perturbative expansion reproducing the expected results within a relative error of 10^(-4). On the strong coupling side we present a supergravity evaluation of the 1/8 BPS correlator in the limit of large separation, taking into account the exchange of all relevant modes between the string world-sheets. While reproducing the correct geometrical dependence, we find that the associated coefficient does not match the localization result.