The Fate of Unstable Gauge Flux Compactifications

TL;DR

This paper investigates the instability and evolution of non-abelian gauge flux compactifications in six dimensions, showing that unstable monopoles tend to decay into stable configurations with specific geometric and stability properties.

Contribution

It demonstrates that unstable monopoles in Einstein-Yang-Mills systems evolve into stable configurations with modified geometries, and explores the endpoint geometries in supergravity models.

Findings

Unstable monopoles decay into stable monopoles with adjusted geometries.

In Einstein-Yang-Mills systems, the geometry shifts from Mink(d)xS2 to AdS(d)xS2.

The endpoint in 6D supergravity is a singular Kasner-like geometry with lower potential energy.

Abstract

Fluxes are widely used to stabilise extra dimensions, but if they arise within a non-abelian gauge sector they are often unstable. We seek the fate of this instability, focussing on the simplest examples: sphere-monopole compactifications in six dimensions. Without gravity most non-abelian monopoles are unstable, decaying into the unique stable monopole in the same topological class. We show that the same is true in Einstein-YM systems, with the geometry adjusting accordingly: a Mink(d)xS2 geometry supported by an unstable monopole relaxes to an AdS(d)xS2. For 6D supergravity, the dilaton obstructs this simple evolution, acquiring a gradient and thus breaking some of the spacetime symmetries. We argue that it is the 4D symmetries that break, and examine several endpoint candidates. Oxidising the supergravity system into a higher-dimensional Einstein-YM monopole, we use the latter to guide us to the corresponding endpoint. The result is a singular Kasner-like geometry conformal to Mink(4)xS2. The solution has lower potential energy and is perturbatively stable, making it a sensible candidate endpoint for the evolution. (Abridged abstract for arXiv.)