Localized tachyons in C^3/Z_N

TL;DR

This paper investigates the process of localized closed string tachyon condensation in non-supersymmetric C^3/Z_N orbifolds, revealing how it leads to various geometric resolutions and smooth endpoints in Type II theories.

Contribution

It provides a detailed analysis of tachyon condensation in C^3/Z_N orbifolds, connecting worldsheet supersymmetry, toric geometry, and the nature of singularity resolutions, including the proof that Type II endpoints are always smooth.

Findings

Tachyon condensation can lead to geometric and codimension two singularities.

Some resolutions are related by flip transitions.

Type II theories always end in smooth spaces, with no residual singularities.

Abstract

We study the condensation of localized closed string tachyons in C^3/Z_N nonsupersymmetric noncompact orbifold singularities via renormalization group flows that preserve supersymmetry in the worldsheet conformal field theory and their interrelations with the toric geometry of these orbifolds. We show that for worldsheet supersymmetric tachyons, the endpoint of tachyon condensation generically includes ``geometric'' terminal singularities (orbifolds that do not have any marginal or relevant Kahler blowup modes) as well as singularities in codimension two. Some of the various possible distinct geometric resolutions are related by flip transitions. For Type II theories, we show that the residual singularities that arise under tachyon condensation in various classes of Type II theories also admit a Type II GSO projection. We further show that Type II orbifolds entirely devoid of marginal or relevant blowup modes (Kahler or otherwise) cannot exist, which thus implies that the endpoints of tachyon condensation in Type II theories are always smooth spaces.