ar X iv : h ep - t h / 02 02 09 7 v 1 1 6 Fe b 20 02 Tachyon mass , c - function and Counting localized degrees of freedom

We discuss the localized tachyon condensation in the non-supersymmetric orbifold theories by taking the cosmological constant as the measure of degrees of freedom. We show that both localized and delocalized degrees of freedom encode information on the process of localized tachyon condensation: the former encodes in the c-function given by the lightest tachyon mass, and the latter in the g-function. For type II, both cand g-function respect the stability of the supersymmetric models. We suggest that physical origin of this phenomena is due to the special property of the orbifolds: the local geometry around the fixed point completely determines the global geometry of the orbifolds.