Tests of Large $N_c$ QCD from Hadronic $\tau$ Decay

We use the ALEPH Collaboration data on vector and axial-vector spectral functions to test simple duality properties of QCD in the large $N_c$ limit, which emerge in the approximation of a minimal hadronic ansatz of a spectrum of narrow states. These duality properties relate the short- and long-distance behaviors of specific correlation functions, which are order parameters of spontaneous chiral symmetry breaking, in a way that we find well supported by the data.