Precision calculation of 1/4-BPS Wilson loops in AdS$_5\times S^5$

TL;DR

This paper investigates the strong coupling behavior of 1/4-BPS Wilson loops in N=4 Super Yang-Mills, computing one-loop string corrections and comparing them with localization results, revealing a discrepancy that suggests further investigation.

Contribution

It provides a detailed one-loop correction calculation for 1/4-BPS Wilson loops in AdS5×S5 and compares these with exact localization results, highlighting a novel discrepancy.

Findings

Discrepancy between string theory calculations and localization results.

Introduction of a remainder function to quantify the mismatch.

Numerical evaluation of functional determinants with complications.

Abstract

We study the strong coupling behaviour of $1/4$-BPS circular Wilson loops (a family of "latitudes") in ${\cal N}=4$ Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS$_5\times$S$^5$. Supersymmetric localization provides an exact result that, in the large 't Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the $ratio$ between the generic latitude and the maximal 1/2-BPS circle: Any measure-related ambiguity should simply cancel in this way. We use Gel'fand-Yaglom method to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: The difference is encoded into a precise "remainder function". We comment on the possible origin and resolution of this discordance.