Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Localized instabilities at conifolds

Angel M. Uranga

TL;DR

This work analyzes how M-theory lifts of intersecting D6-branes at angles host localized instabilities that dynamically drive topology-changing transitions, such as conifold transitions between small resolutions and deformations. By deploying BPS-based energetics, the authors show that non-supersymmetric configurations exhibit a dynamical smoothing process localized at singularities, while compact models can stabilize at finite, often supersymmetric endpoints without reducing spacetime dimensions. The study connects brane recombination in type II string theory to geometric transitions in Calabi–Yau and $G_2$ geometries via Taub–NUT and conifold constructions, providing a unified picture across one-, two-, and three-angle systems. These insights illuminate purely gravitational dynamics in string/M-theory and hint at broader roles for localized instabilities in moduli stabilization and topology change.

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.

Localized instabilities at conifolds

TL;DR

This work analyzes how M-theory lifts of intersecting D6-branes at angles host localized instabilities that dynamically drive topology-changing transitions, such as conifold transitions between small resolutions and deformations. By deploying BPS-based energetics, the authors show that non-supersymmetric configurations exhibit a dynamical smoothing process localized at singularities, while compact models can stabilize at finite, often supersymmetric endpoints without reducing spacetime dimensions. The study connects brane recombination in type II string theory to geometric transitions in Calabi–Yau and geometries via Taub–NUT and conifold constructions, providing a unified picture across one-, two-, and three-angle systems. These insights illuminate purely gravitational dynamics in string/M-theory and hint at broader roles for localized instabilities in moduli stabilization and topology change.

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 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.

Paper Structure

This paper contains 12 sections, 28 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Two angle system
  3. System of D6-branes intersecting over 5d
  4. Energetics in the M-theory lift
  5. The dynamical conifold transition
  6. Discussion of compact models
  7. One- and three-angle systems
  8. One angle system
  9. Three angle case
  10. Conclusions
  11. Recombined special lagrangian cycles
  12. Kähler constraints in conifold transitions from D6-branes

Figures (5)

  • Figure 1: Schematic picture of the lift of configurations of D6-branes intersecting at two angles on the Coulomb (a) and Higgs (b) branch. They are related by a topology changing conifold transition. We have highlighted the non-trivial two- and three-spheres in these geometries, which are obtained as $\bf S^1$ fibrations over a segment (a) and a disk (b) on the base.
  • Figure 2: Phase transition in the M-theory lift of intersecting D6-branes a) in the small circle limit (weakly coupled IIA) and b) in the large circle regime. Even though the nature of the instability is not fully understood (lies beyond supergravity due to small cycles) it certainly mediates a dynamical conifold transition transforming an initially large 2-cycle into a finally large 3-cycle.
  • Figure 3: Schematic picture of the lift of configurations of D6-branes intersecting at one angle on the Coulomb (a) and Higgs (b) branch. We have highlighted the two different non-trivial two-spheres in these geometries, which are obtained as $\bf S^1$ fibrations over two different segments on the base.
  • Figure 4: Intersecting D6-branes provide a skeleton picture for certain Calabi-Yau threefolds with conifold singularities. The shaded area provides the skeleton picture for a 3-chain defining a homology relation between 2-spheres A, C, in the small resolution phase. This homology relaton allows a conifold transition involving the corresponding nodes.
  • Figure 5: The 3-chain $\Sigma_3$ mentioned in figure \ref{['homology']} is obtained by fibering the M-theory circle over the region here depicted. Notice that the 2-spheres at the two locations B are glued onto each other, and do not belong to the boundary of $\Sigma_3$.