On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze

TL;DR

This paper explores the integrability of Wilson loops in AdS_5 x S^5 by applying techniques from spinning string solutions to find minimal surfaces with periodic boundary conditions, revealing diverse solutions and phases.

Contribution

It extends integrability methods from spinning strings to a broad class of Wilson loops with periodic boundary conditions, uncovering new solutions and phases.

Findings

Identified a rich variety of Wilson loop solutions with periodic boundary conditions.

Analyzed different phases and their implications for integrability.

Discussed the applicability of integrability to general Wilson loop problems.

Abstract

Wilson loops are calculated within the AdS/CFT correspondence by finding a classical solution to the string equations of motion in AdS_5 x S^5 and evaluating its action. An important fact is that this sigma-model used to evaluate the Wilson loops is integrable, a feature that has gained relevance through the study of spinning strings carrying large quantum numbers and spin-chains. We apply the same techniques used to solve the equations for spinning strings to find the minimal surfaces describing a wide class of Wilson loops. We focus on different cases with periodic boundary conditions on the AdS_5 and S^5 factors and find a rich array of solutions. We examine the different phases that appear in the problem and comment on the applicability of integrability to the general problem.