On the Delta I = 1/2 Rule in Holographic QCD

We study the $\mathrm{\Delta }I=1\mathrm{/}2$ rule for kaon decays and the $B_K$ parameter for $K^0-{\bar{K}}^0$ mixing in a dual 5-dimensional holographic QCD model. We perform, in the chiral limit, computations of the relevant four-point current-current correlators, which depend upon self-interactions among the 5D bulk fields. Spontaneous chiral symmetry breaking ($\chi$SB) is realized through boundary conditions on the bulk fields. Numerical results are analyzed in comparison with QCD, chiral perturbation theory ($\chi$PT) and data, finding reasonable agreement with the experimental values of the $g_8$ and $g_{27}$ parameters describing the $\mathrm{\Delta }I=1\mathrm{/}2,3\mathrm{/}2$ decay channels.