D-Branes on Calabi-Yau Spaces and Their Mirrors

TL;DR

This paper investigates the boundary states of D-branes on Calabi-Yau spaces, exploring their geometric encoding, mirror symmetry transformations, and implications for instanton corrections, enhancing understanding of string dualities.

Contribution

It provides a detailed analysis of how D-brane boundary states encode geometric data and how mirror symmetry acts on these states, including T-duality cases.

Findings

Mirror symmetry transforms D-branes consistently with monodromy.

Boundary states encode geometric data of supersymmetric cycles.

Open string instanton corrections relate to closed string instanton counting.

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.