Stability of Quiver Representations and Topology Change

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.

16 pages, 7 figures, minor corrections, references added

References in corpus (2)

• Derived Categories and Zero-Brane Stability
• The BPS Spectrum of N=2 SU(N) SYM and Parton Branes

Cited by in corpus (8)

• Dimer models and toric diagrams
• Symmetries of Toric Duality
• The Master Space of N=1 Gauge Theories
• Quiver Gauge Theory and Conformality at the TeV Scale
• Master Space and Hilbert Series for N=1 Field Theories
• D-geometric Structure of Orbifolds
• A relation between moduli space of D-branes on orbifolds and Ising model
• Moduli of McKay quiver representations I: the coherent component