Small-size instanton corrections to the $\tau$ hadronic width

We compute the effect of small-size instanton corrections to current-current correlators, for all combinations of axial, vector, and possibly flavour non-diagonal currents. We apply our result to the hadronic decays of the $\tau$ lepton, in order to assess the reliability of the determination of $\alpha_s$ from the $\tau$ hadronic width.