Supersymmetric Wilson loops at two loops

Details Supersymmetric Wilson loops at two loops Supersymmetric Wilson loops at two loops

2008-04-24

arxiv.org/abs/0804.3973v2

JHEP0806:083,2008

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, 14 figures, typos corrected, references added

Scientific paper

10.1088/1126-6708/2008/06/083

We study the quantum properties of certain BPS Wilson loops in ${\cal N}=4$ supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on $S^3$ with a fraction of supersymmetry. When restricted to $S^2$, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM$_2$ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.

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