Stability Conditions and Branes at Singularities

TL;DR

This paper explores the stability of D-branes at Calabi-Yau singularities using Bridgeland stability conditions, proving decay processes and properties of certain sheaves, which aids in deriving quiver gauge theories from branes.

Contribution

It applies Bridgeland's stability framework to D-branes on Calabi-Yau cones, demonstrating brane decay and analyzing sheaf representations, advancing understanding of branes at singularities.

Findings

Decay of D3-branes into fractional branes proven

Existence of stability conditions on Calabi-Yau cones established

Skyscraper sheaves off the zero section are simple representations

Abstract

I use Bridgeland's definition of a stability condition on a triangulated category to investigate the stability of D-branes on Calabi-Yau cones given by the canonical line bundle over a del Pezzo surface. In this context, I prove the existence of the decay of a D3-brane into a set of fractional branes. This is an important aspect of the derivation of quiver gauge theories from branes at singularities via the technique of equivalences of categories. Some important technical aspects of this equivalence are discussed. I also prove that the representations corresponding to skyscraper sheaves supported off the zero section are simple.