  We present a lattice QCD calculation of the axial $\gamma W$-box diagrams
relevant for the kaon semileptonic decays. We utilize a recently proposed
method, which connects the electroweak radiative corrections in Sirlin's
representation to that in chiral perturbation theory. It allows us to use the
axial $\gamma W$-box correction in the SU(3) limit to obtain the low energy
constants for chiral perturbation theory. From first principles our results
confirm the previously used low energy constants provided by the minimal
resonance model with a significant reduction in uncertainties.
