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We study the predictions of holographic QCD for various observable four-pointquark flavour current-current correlators. The dual 5-dimensional bulk theorywe consider is a $SU(3)_L \times SU(3)_R$ Yang Mills theory in a slice of$AdS_5$ spacetime with boundaries. Particular UV and IR boundary conditionsencode the spontaneous breaking of the dual 4D global chiral symmetry down tothe $SU(3)_V$ subgroup. We explain in detail how to calculate the 4D four-pointquark flavour current-current correlators using the 5D holographic theory,including interactions. We use these results to investigate predictions ofholographic QCD for the $\Delta I = 1/2$ rule for kaon decays and the $B_K$parameter. The results agree well in comparison with experimental data, with anaccuracy of 25% or better. The holographic theory automatically includes thecontributions of the meson resonances to the four-point correlators. Thecorrelators agree well in the low-momentum and high-momentum limit, incomparison with chiral perturbation theory and perturbative QCD results,respectively.Comment: Published version, title changed to conform with Journal format,  references and clarifying remarks added, 40 pages, 5 figure

Four-point functions and kaon decays in a minimal AdS/QCD model