The spectrum of BPS branes on a noncompact Calabi-Yau

TL;DR

This paper explores the spectrum of BPS branes on a noncompact Calabi-Yau space, analyzing how it varies across different stability lines and connecting descriptions near large volume and orbifold points.

Contribution

It provides a comprehensive analysis of BPS brane spectra on a specific noncompact Calabi-Yau, revealing similarities between different limits and proposing a generalized framework.

Findings

Complete BPS spectrum near large volume limit

Complete BPS spectrum near orbifold point

Identified similarities between holomorphic bundles and BPS branes

Abstract

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to C^3/Z_3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.