Three-point current correlation functions as probes of effective conformal theories

The first sub-leading, order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {1 \left/ {{\sqrt{\lambda }}} \right.} $\end{document} correction to the three-point current correlation function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \left\langle {J_i^a(x)J_j^b(y)J_k^c(z)} \right\rangle $\end{document} of a strongly coupled conformal system with non-Abelian global symmetry is shown to come uniquely from the non-renormalizable bulk operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\left( {{F_{{\mu \nu }}}} \right)}^3} $\end{document}. The non-renormalizable correction is suppressed by powers of the cutoff scale Λ of the bulk effective theory, which corresponds to a dimension cutoff Δ = RAdSΛ in the boundary effective conformal theory. The contribution of the non-renormalizable term to the three-point function is calculated from the weakly coupled AdS dual in the large N limit. It is shown to have a polarization structure different from the leading contribution, which comes from the renormalizable \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\left( {{F_{{\mu \nu }}}} \right)}^2} $\end{document} operator. This suggests a possible experimental probe of the effective conformal description through a measurement of the cutoff dimension Δ in strongly coupled condensed matter systems.