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We review and update our results for K-> pipi decays and K^0-\bar K^0 mixingobtained by us in the 1980s within an approach based on the dual representationof QCD as a theory of weakly interacting mesons for large N colours. In ouranalytic approach the dynamics behind the enhancement of ReA_0 and suppressionof ReA_2, the so-called Delta I = 1/2 rule for K-> pi pi decays, has a simplestructure: the usual octet enhancement through quark-gluon renormalizationgroup evolution down to the scales O(1 GeV) is continued as a meson evolutiondown to zero momentum scales at which the factorization of hadronic matrixelements is at work. The inclusion of lowest-lying vector meson contributionsin addition to the pseudoscalar ones and of Wilson coefficients in a momentumscheme improves significantly the matching between quark-gluon and mesonevolutions. In particular, the anomalous dimension matrix governing the mesonevolution exhibits the structure of the known anomalous dimension matrix in thequark-gluon evolution. The recent results on ReA_2 and ReA_0 from the RBC-UKQCcollaboration give support for our approach. In particular, the signs of thetwo main contractions found numerically by these authors follow uniquely fromour analytic approach. At NLO in 1/N we obtain ReA_0/ReA_2= 16.0\pm 1.5 whichamounts to an order of magnitude enhancement over the strict large N limitvalue sqrt{2}. QCD penguins contribute at 15% level to this result. We alsofind \hat B_K=0.73\pm 0.02, with the smallness of 1/N corrections to the largeN value \hat B_K=3/4 resulting within our approach from an approximatecancellation between pseudoscalar and vector meson one-loop contributions. Wesummarize the status of Delta M_K in this approach.

Large N Approach to Kaon Decays and Mixing 28 Years Later: Delta I = 1/2 Rule, \hat B_K and Delta M_K