Localized instabilities at conifolds

TL;DR

This paper explores how certain geometric transitions in M-theory, related to D6-branes and conifold singularities, involve localized instabilities that can lead to topology change and phase transitions, both in supersymmetric and non-supersymmetric contexts.

Contribution

It provides a detailed analysis of localized instabilities at conifold singularities in M-theory lifts of D6-brane configurations, including non-supersymmetric cases and their implications for topology-changing transitions.

Findings

Instabilities are localized at singularities and can drive topology change.

Non-supersymmetric configurations can be reliably lifted, showing similar transition behavior.

In compact setups, instabilities can relax to stable minima, leading to well-defined decay endpoints.

Abstract

We consider the M-theory lifts of configurations of type IIA D6-branes intersecting at angles. In supersymmetry preserving cases, the lifts correspond to special holonomy geometries, like conifolds and $G_2$ holonomy singularities. Transitions in which D6-branes approach and recombine lift to topology changing transition in these geometries. In some instances non-supersymmetric configurations can be reliably lifted, leading to the same topological manifolds, but endowed with non-supersymmetric metrics. In these cases the phase transitions are driven dynamically, due to instabilities localized at the singularities. Even though in non-compact setups the instabilities relax to infinity, in compact situations there exist nearby minima where the instabilities dissappear and the decay reaches a well-defined (in general supersymmetric) endpoint.