Don't Panic! Closed String Tachyons in ALE Spacetimes

TL;DR

This paper investigates how localized closed string tachyons in noncompact orbifolds induce decay processes that lead to supersymmetric ALE spaces or flat space, supported by evidence from D-brane probes, worldsheet RG flow, and spacetime gravity.

Contribution

It demonstrates that closed string tachyon condensation drives non-supersymmetric orbifolds to supersymmetric ALE spaces, revealing a new decay mechanism and connecting to duality conjectures.

Findings

Tachyon condensation results in a transition to supersymmetric ALE spaces.

Evidence from D-brane probes and worldsheet RG flow supports the decay process.

Mechanism for creating NS5-branes via closed string tachyon condensation.

Abstract

We consider closed string tachyons localized at the fixed points of noncompact nonsupersymmetric orbifolds. We argue that tachyon condensation drives these orbifolds to flat space or supersymmetric ALE spaces. The decay proceeds via an expanding shell of dilaton gradients and curvature which interpolates between two regions of distinct angular geometry. The string coupling remains weak throughout. For small tachyon VEVs, evidence comes from quiver theories on D-branes probes, in which deformations by twisted couplings smoothly connect non-supersymmetric orbifolds to supersymmetric orbifolds of reduced order. For large tachyon VEVs, evidence comes from worldsheet RG flow and spacetime gravity. For $\IC^2/\IZ_n$, we exhibit infinite sequences of transitions producing SUSY ALE spaces via twisted closed string condensation from non-supersymmetric ALE spaces. In a $T$-dual description this provides a mechanism for creating NS5-branes via {\it closed} string tachyon condensation similar to the creation of D-branes via {\it open} string tachyon condensation. We also apply our results to recent duality conjectures involving fluxbranes and the type 0 string.