Abstract
The first sub-leading, order $ {1 \left/ {{\sqrt{\lambda }}} \right.} $ correction to the three-point current correlation function $ \left\langle {J_i^a(x)J_j^b(y)J_k^c(z)} \right\rangle $ of a strongly coupled conformal system with non-Abelian global symmetry is shown to come uniquely from the non-renormalizable bulk operator $ {{\left( {{F_{{\mu \nu }}}} \right)}^3} $ . 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 = R AdSΛ 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 $ {{\left( {{F_{{\mu \nu }}}} \right)}^2} $ 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.
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