D-branes on Orbifolds and Topology Change

TL;DR

This paper explores the topology and phase structure of D-branes on orbifolds using toric geometry, revealing multiple topologically distinct phases and the projection of non-geometric phases for specific orbifold cases.

Contribution

It introduces a detailed analysis of D-brane moduli spaces on orbifolds, identifying multiple phases and their topological relations, including resolutions of singularities.

Findings

Five distinct phases for n=11 orbifold

Topological transitions via flops between phases

Projection of non-geometric phases for n=7,9,11

Abstract

We consider D-branes on an orbifold $C^3/Z_n$ and investigate the moduli space of the D-brane world-volume gauge theory by using toric geometry and gauged linear sigma models. For $n=11$, we find that there are five phases, which are topologically distinct and connected by flops to each other. We also verify that non-geometric phases are projected out for $n=7,9,11$ cases as expected. Resolutions of non-isolated singularities are also investigated.