D-branes on some one- and two-parameter Calabi-Yau hypersurfaces

TL;DR

The paper investigates D-branes on one-parameter Calabi-Yau hypersurfaces and two-parameter K3-fibered Calabi-Yau manifolds from both Gepner-model boundary states and geometric perspectives. By analyzing periods of the holomorphic three-form, basis changes between Gepner and large-volume descriptions, and Mukai-vector data, it builds a concrete dictionary linking BPS brane spectra at the Gepner point to geometric branes at large volume. It demonstrates how D0-branes can be present or absent at the Gepner point, identifies various bound states (D6–D0, D4–D2) and their moduli, and explains phase transitions under moduli evolution, including supersymmetry-breaking decays interpreted via mirror symmetry and T-duality. The work provides explicit computations of intersection forms, Witten indices, and boundary-state data for the studied models, offering a detailed framework for translating between exactly solvable CFT data and geometric D-brane physics in Calabi-Yau compactifications.

Abstract

D-branes on one-parameter Calabi-Yau spaces and two-parameter K3-fibered Calabi-Yau manifolds are analyzed from both the Gepner model point of view and the geometric perspective. We compute part of the spectrum of the boundary states and comment on the appearance of the D0-brane as well as on nonsupersymmetric large volume configurations becoming supersymmetric at the Gepner point.