Correlation function of null polygonal Wilson loops with local operators

We consider the correlator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{{\left\langle {{W_n}\mathcal{O}} \right\rangle }} \left/ {{\left\langle {{W_n}} \right\rangle }} \right.} $\end{document} of a light-like polygonal Wilson loop with n cusps with a local operator (like the dilaton or a chiral primary scalar) in planar \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \mathcal{N} = 4 $\end{document} super Yang-Mills theory. As a consequence of conformal symmetry, the main part of such correlator is a function F of 3n − 11conformal ratios. The first non-trivial case is n = 4 when F depends on just one conformal ratio ζ. This makes the corresponding correlator one of the simplest non-trivial observables that one would like to compute for generic values of the ‘t Hooft coupling λ. We compute F(ζ, λ) at leading order in both the strong coupling regime (using semiclassical AdS5 × S5 string theory) and the weak coupling regime (using perturbative gauge theory). Some results are also obtained for polygonal Wilson loops with more than four edges. Furthermore, we also discuss a connection to the relation between a correlator of local operators at null-separated positions and cusped Wilson loop suggested in arXiv:1007.3243.