Stability of Quiver Representations and Topology Change

TL;DR

This paper investigates the phase structure of D0-brane moduli spaces on orbifolds using quiver representations and toric geometry, revealing correspondences and explaining the emergence of geometric phases.

Contribution

It establishes a detailed correspondence between quiver stability conditions and toric geometric phases, clarifying the role of coordinate redundancies and monodromy effects.

Findings

Multiple phases connected by flop transitions identified.

Redundancy in toric coordinates explains disappearance of non-geometric phases.

Only geometric phases emerge from D0-brane stability analysis.

Abstract

We study phase structure of the moduli space of a D0-brane on the orbifold C^3/Z_2 \times Z_2 based on stability of quiver representations. It is known from an analysis using toric geometry that this model has multiple phases connected by flop transitions. By comparing the results of the two methods, we obtain a correspondence between quiver representations and geometry of toric resolutions of the orbifold. It is shown that a redundancy of coordinates arising in the toric description of the D-brane moduli space, which is a key ingredient of disappearance of non-geometric phases, is understood from the monodromy around the orbifold point. We also discuss why only geometric phases appear from the viewpoint of stability of D0-branes.