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

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.