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Supersymmetric Wilson loops at two loops

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arxiv 0804.3973 v2 pith:DPG55J2F submitted 2008-04-24 hep-th

classification hep-th
keywords loopswilsonquantumspheresupersymmetricadditionagreementanalysis
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

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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  1. Correlators in non-conformal $\mathcal{N}=2$ gauge theories from localization

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    Two-point correlators of chiral/anti-chiral operators in SU(N) N=2 gauge theories with a non-zero beta function, computed by Feynman diagrams in flat space, match sphere-localization matrix model results exactly throu...

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