Bubbles of Nothing and Supersymmetric Compactifications

TL;DR

This paper explores the non-perturbative stability of supersymmetric compactifications against bubble of nothing decay, revealing a dynamical suppression mechanism that enforces stability even when topological obstructions are absent.

Contribution

It demonstrates a new dynamical suppression mechanism preventing decay of supersymmetric vacua in topologically unobstructed cases, supported by a four-dimensional supergravity toy model.

Findings

Supersymmetric compactifications can be unstable to bubble of nothing decay without topological obstructions.

A suppression mechanism analogous to Coleman-De Luccia prevents decay near the supersymmetric limit.

The circumference of the bubble diverges as supersymmetry is approached, halting decay.

Abstract

We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such "topologically unobstructed" cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to $M_3 \times S_1$ presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this decay. This demonstrates the dynamical origin of the decay suppression, as opposed to the more familiar argument based on the spin structure. We conjecture that this is a generic mechanism that enforces stability of any topologically unobstructed supersymmetric compactification.