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

Abstract

We study the correlators of a recently discovered family of BPS Wilson loops in = 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 (g4) 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 (g6). 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. At strong coupling we compare our result to the string dual of the = 4 SYM correlator in the limit of large separation, presenting some preliminary evidence for the agreement.