Abstract
We study the predictions of holographic QCD for various observable four-point quark-flavor current-current correlators. The dual 5-dimensional bulk theory we consider is a $SU(3{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(3{)}_{R}$ Yang-Mills theory in a slice of $\mathrm{Ad}{\mathrm{S}}_{5}$ spacetime with boundaries. Particular UV and IR boundary conditions encode the spontaneous breaking of the dual 4D global chiral symmetry down to the $SU(3{)}_{V}$ subgroup. We explain in detail how to calculate the 4D four-point quark-flavor current-current correlators using the 5D holographic theory, including interactions. We use these results to investigate predictions of holographic QCD for the $\ensuremath{\Delta}I=1/2$ rule for kaon decays and the ${B}_{K}$ parameter. The results agree well in comparison with experimental data, with an accuracy of 25% or better. The holographic theory automatically includes the contributions of the meson resonances to the four-point correlators. The correlators agree well in the low-momentum and high-momentum limit, in comparison with chiral perturbation theory and perturbative QCD results, respectively.
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