Brane Cube Realization of Three-dimensional Nonabelian Orbifolds

TL;DR

This paper constructs three-dimensional brane configurations for nonabelian orbifolds of the form ${f C}^3/ ext{group}$, revealing new geometric structures and relationships between branes and orbifold groups.

Contribution

It introduces a novel three-dimensional brane configuration framework for nonabelian orbifolds of ${f C}^3$, extending previous two-dimensional models.

Findings

Constructed brane configurations for ${f C}^3/ ext{group}$ orbifolds.

Established correspondence between quiver diagrams and three-dimensional brane setups.

Derived configurations for nonabelian orbifolds via quotienting procedures.

Abstract

We study D-branes on three-dimensional orbifolds ${\bf C}^3/\Gamma$ where $\Gamma$ are finite subgroups of SU(3). The quiver diagram of $\ZnZn \in SU(3)$ can be expressed in three-dimensional form. According to the correspondence between quiver diagrams and brane configurations, we construct a brane configuration for ${\bf C}^3/\ZnZn$ which has essentially three-dimensional structrue. Brane configurations for nonabelian orbifolds $\C^3/\Delta(3n^2)$ and $\C^3/\Delta(6n^2)$ are obtained from that for $\C^3/\ZnZn$ by certain quotienting procedure.