Special contact Wilson loops

Details Special contact Wilson loops Special contact Wilson loops

2002-11-24

arxiv.org/abs/hep-th/0211229v2

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, LaTeX, references added, small corrections in Section 4

Scientific paper

Wilson loops in ${\cal N}=4$ supersymmetric Yang-Mills theory correspond at strong coupling to extremal surfaces in $AdS_5$. We study a class of extremal surfaces known as special Legendrian submanifolds. The "hemisphere" corresponding to the circular Wilson loop is an example of a special Legendrian submanifold, and we give another example. We formulate the necessary conditions for the contour on the boundary of $AdS_5$ to be the boundary of the special Legendrian submanifold and conjecture that these conditions are in fact sufficient. We call the solutions of these conditions "special contact Wilson loops". The first order equations for the special Legendrian submanifold impose a constraint on the functional derivatives of the Wilson loop at the special contact contour which should be satisfied in the Yang-Mills theory at strong coupling.

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