Collapsing D-branes in one-parameter models and small/large radius duality

TL;DR

This paper completes the analysis of collapsing D-branes in one-parameter Calabi-Yau models, providing evidence for generic collapsing 6-branes at conifold points and revealing an exotic small-large radius duality linked to a discrete symmetry.

Contribution

It advances the understanding of collapsing D-branes by completing the hypergeometric hierarchy analysis and identifying a novel small-large radius duality in one-parameter models.

Findings

Collapse of 6-branes at conifold points is generic.

Identification of an exotic small-large radius duality.

Implementation of discrete symmetry as exchange of Lagrangian fibrations.

Abstract

We finalize the study of collapsing D-branes in one-parameter models by completing the analysis of the associated hypergeometric hierarchy. This brings further evidence that the phenomenon of collapsing 6-branes at the mirror of the `conifold' point in IIA compactifications on one-parameter Calabi-Yau manifolds is generic. It also completes the reduction of the study of higher periods in one-parameter models to a few families which display characteristic behaviour. One of the models we consider displays an exotic form of small-large radius duality, which is a consequence of an ``accidental'' discrete symmetry of its moduli space. We discuss the implementation of this symmetry at the level of the associated type II string compactification and its action on D-brane states. We also argue that this model admits two special Lagrangian fibrations and that the symmetry can be understood as their exchange.