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

Understand

We study the correlators of a recently discovered family of BPS Wilson loops in ${\cal N}=4$ supersymmetric U(N) Yang-Mills theory.

• When the contours lie on a two-sphere in the space-time, we propose a closed expression that is valid for all values of the coupling constant $g$ and for any rank $N$, by exploiting the suspected relation with two-dimensional gauge theories.
• We check this formula perturbatively at order ${\cal O}(g^4)$ for two latitude Wilson loops and 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 and suggests the existence of a peculiar protected local operator arising in the OPE of the Wilson loop.