D-Branes on Calabi-Yau Spaces and Their Mirrors

TL;DR

This work builds a conformal-field-theory framework to describe D-branes wrapped on supersymmetric cycles in Calabi-Yau manifolds via boundary states, uncovering how geometric data are encoded in boundary-state coefficients. It explicitly analyzes how mirror symmetry maps D-brane configurations and RR fields, verifying consistency with integral structures and monodromy, and elucidates the interplay between open-string instantons and closed-string instanton counting. The authors also illustrate the formalism with concrete examples including T-duality on tori and CY orbifolds, and discuss the role of extended worldsheet supersymmetry in realizing certain cycle types. Overall, the paper links boundary-state data to geometric cycles, illuminates mirror-transformed brane configurations, and reveals deep connections between open and closed string sectors in CY compactifications.

Abstract

We study the boundary states of D-branes wrapped around supersymmetric cycles in a general Calabi-Yau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms D-branes, and we verify that it is consistent with the conjectured periodicity and the monodromy of the Ramond-Ramond field configuration on a Calabi-Yau manifold. This also enables us to study open string worldsheet instanton corrections and relate them to closed string instanton counting. The cases when the mirror symmetry is realized as T-duality are also discussed.