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

Nadav Drukker; Bartomeu Fiol

doi:10.1088/1126-6708/2006/01/056

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

Nadav Drukker·Bartomeu Fiol

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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.

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Nadav Drukker, Bartomeu Fiol. 2005-06-07. On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze. https://doi.org/10.1088/1126-6708%2F2006%2F01%2F056

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