D-branes on Calabi-Yau manifolds and helices

TL;DR

This paper explores the relationship between D-branes on Calabi-Yau manifolds in different limits, proposing a new computational method for the McKay correspondence and examining the roles of helices and Beilinson's theorem.

Contribution

It introduces a novel procedure to improve the McKay correspondence computation and analyzes the significance of helices in the context of D-branes on Calabi-Yau manifolds.

Findings

Proposed a new computational method for McKay correspondence

Proved the method in a non-trivial example

Discussed the relevance of helices and connections to Beilinson's theorem

Abstract

We investigate further on the correspondence between branes on a Calabi-Yau in the large volume limit and in the orbifold limit. We conjecture a new procedure which improves computationally the McKay correspondence and prove it in a non trivial example. We point out the relevance of helices and try to draw some general conclusions about Beilinson theorem and McKay correspondence.