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Three-point current correlation functions as probes of Effective Conformal Theories

The three-point current correlation function in Euclidean spacetime for a strongly coupled system with non-Abelian global symmetry, $\langle J^a_i(x)J^b_j(y)J^c_k(z)\rangle$, is calculated from the weakly coupled AdS dual. The contribution from the first non-renormalizable bulk operator, $(F_{μν})^3$, is calculated and shown to lead to a polarization structure different from the leading contribution, which comes from the renormalizable $(F_{μν})^2$ operator. The non-renormalizable correction is suppressed by powers of the cutoff scale $Λ$. This suggests a possible experimental probe of the effective description through a measurement of the cutoff scale $Λ$ in strongly coupled condensed matter systems.