Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in $tau$-decay analyses. Using an $SU(3)_Lotimes SU(3)_R$ decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio $varepsilon/varepsilon$, using the measured hadronic spectral functions in $tau$ decay. Second, we fit our $SU(3)$ dynamical parameters to the most recent lattice data on $Ktopipi$ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the $Delta I = frac{1}{2}$ enhancement, confirming old suggestions about its underlying dynamical origin.
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