Tachyon mass, c-function and Counting localized degrees of freedom

TL;DR

This paper introduces a c-function based on the lightest tachyon mass to measure localized degrees of freedom in non-supersymmetric orbifolds, linking tachyon condensation to the tachyon potential and geometric properties.

Contribution

It proposes a new c-function derived from the lightest tachyon mass for counting localized degrees of freedom in orbifold theories, connecting it to the tachyon potential and geometric analysis.

Findings

Localized d.o.f. are better measured by the c-function from tachyon mass.

The c-function matches the recently proposed tachyon potential.

Both c- and g-functions reflect stability and processes in supersymmetric models.

Abstract

We discuss the localized tachyon condensation in the non-supersymmetric orbifold theories by taking the cosmological constant as the measure of degrees of freedom (d.o.f). We first show asymptotic density of state is not a proper quantity to count the 'localized' d.o.f. We then show that localized d.o.f lead us a c-function given by the lightest tachyon mass, which turns out to be the same as the tachyon potential recently suggested by Dabholkar and Vafa. We also argue that delocalized d.o.f also encode information on the process of localized tachyon condensation in the g-function, based on the fact that the global geometry of the orbifolds is completely determined by the local geometry around the fixed points. For type II, both c- and g-function respect the stability of the supersymmetric models and both allow all the process suggested by Adams, Polchinski and Silverstein.