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 (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 (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. 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. © SISSA 2009.