On the integrability of Wilson loops inAdS5×S5: some periodic ansatze

2005/06/07 by Nadav Drukker, Bartomeu Fiol
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1088/1126-6708/2006/01/056

published as JHEP 0601 (2006) 056 · LaTex, 49 pages, 8 figures

arxiv created 2005/06/07 · openalex publication_date 2006/01/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Wilson loops are calculated within the AdS/CFT correspondence by finding a classical solution to the string equations of motion in AdS₅ x S⁵ 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 AdS₅ and S⁵ 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.

Citations

• An exact prediction of N=4 supersymmetric Yang–Mills theory for string theory
• Separation of variables for the classical and quantum Neumann model
• Aspects of semiclassical strings in AdS5
• All-genus calculation of Wilson loops using D-branes
• The dilatation operator of N=4 super Yang–Mills theory and integrability