Orbifold Resolution by D-Branes

TL;DR

This paper investigates the topological and geometric properties of D-brane resolutions of three-dimensional orbifold singularities, revealing how the D-brane vacuum moduli space describes the background spacetime and is controlled by Fayet--Iliopoulos parameters.

Contribution

It demonstrates that the D-brane vacuum moduli space fills the background spacetime and can be described by a gauged linear sigma model that excludes non-geometric phases.

Findings

The D-brane vacuum moduli space corresponds to the background spacetime.

Fayet--Iliopoulos parameters control the size of the blow-ups.

The gauged linear sigma model is non-generic, projecting out non-geometric regions.

Abstract

We study topological properties of the D-brane resolution of three-dimensional orbifold singularities, C^3/Gamma, for finite abelian groups Gamma. The D-brane vacuum moduli space is shown to fill out the background spacetime with Fayet--Iliopoulos parameters controlling the size of the blow-ups. This D-brane vacuum moduli space can be classically described by a gauged linear sigma model, which is shown to be non-generic in a manner that projects out non-geometric regions in its phase diagram, as anticipated from a number of perspectives.