Calculations for Mirror Symmetry with D-branes

TL;DR

This paper investigates D-brane superpotentials on Calabi-Yau hypersurfaces using mirror symmetry, revealing new Picard-Fuchs extensions and a novel topology-changing phase transition involving quantum D-branes.

Contribution

It introduces new classes of Picard-Fuchs equations and uncovers a novel topology-changing phase transition related to quantum D-branes.

Findings

Identification of new Picard-Fuchs extensions

Discovery of a topology-changing phase transition involving quantum D-branes

Analysis of D-brane superpotentials on Calabi-Yau hypersurfaces

Abstract

We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using mirror symmetry in the large volume regime, albeit without identifying the precise A-model geometry in all cases. We identify new classes of extensions of Picard-Fuchs equations, as well as a novel type of topology changing phase transition involving quantum D-branes. A 4-d domain wall which is obtained in one region of closed string moduli space from wrapping a four-chain interpolating between two Lagrangian submanifolds is, for other values of the parameters, represented by a disk ending on a single Lagrangian.