D-branes on a Noncompact Singular Calabi-Yau Manifold

TL;DR

This paper studies D-branes on a noncompact singular Calabi-Yau manifold using boundary conformal field theory, providing geometric interpretations and calculating open string indices to understand their properties.

Contribution

It introduces a boundary CFT approach to analyze D-branes on singular Calabi-Yau manifolds and relates boundary states to geometric coherent sheaves.

Findings

B-type D-branes characterized by properties of a compact positively curved manifold

Calculated open string Witten indices between boundary states

Provided geometric interpretations of boundary states in terms of coherent sheaves

Abstract

We investigate D-branes on a noncompact singular Calabi-Yau manifold by using the boundary CFT description, and calculate the open string Witten indices between the boundary states. The B-type D-branes turn out to be characterized by the properties of a compact positively curved manifold. We give geometric interpretations to these boundary states in terms of coherent sheaves of the manifold.