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We study the correlators of a recently discovered family of BPS Wilson loopsin ${\cal N}=4$ supersymmetric U(N) Yang-Mills theory. When the contours lie ona two-sphere in the space-time, we propose a closed expression that is validfor all values of the coupling constant $g$ and for any rank $N$, by exploitingthe suspected relation with two-dimensional gauge theories. We check thisformula perturbatively at order ${\cal O}(g^4)$ for two latitude Wilson loopsand we show that, in the limit where one of the loops shrinks to a point,logarithmic corrections in the shrinking radius are absent at ${\cal O}(g^6)$.This last result strongly supports the validity of our general expression andsuggests the existence of a peculiar protected local operator arising in theOPE of the Wilson loop. At strong coupling we compare our result to the stringdual of the ${\cal N}=4$ SYM correlator in the limit of large separation,presenting some preliminary evidence for the agreement.

Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM