D-branes at Singular Curves of Calabi-Yau Compactifications

TL;DR

This work extends boundary-conformal-field-theory constructions of D-branes at Gepner points by incorporating twisted sectors associated with singular curves on Calabi–Yau manifolds. By using simple current orbifolds, it first builds untwisted D-branes in Gepner models and then identifies and constructs twisted boundary states that carry RR charges from twisted $(c,c)$-fields, corresponding to branes wrapping exceptional cycles created by resolving ${\mathbb Z}_2$ (and, conjecturally, higher ${\mathbb Z}_{N}$) singularities over curves. The key result is explicit boundary states in the Gepner framework that are charged under twisted sectors, providing a richer D-brane spectrum and a CFT realization of desingularization phenomena. This enhances the understanding of open-string sectors and offers tests of mirror symmetry in open strings, with potential generalizations to B-type branes and higher-order singularities.

Abstract

We study the Gepner model description of D-branes in Calabi-Yau manifolds with singular curves. From a geometrical point of view, the resolution of singularities leads to additional homology cycles around which branes can wrap. Using techniques from conformal field theory we address the construction of boundary states for branes wrapping additional 3-cycles on the resolved Calabi-Yau manifold. Explicit formulas are provided for Z_2 singular curves.