Brane Configurations for Three-dimensional Nonabelian Orbifolds

Abstract

We study brane configurations corresponding to D-branes on complex three-dimensional orbifolds ${\bf C}^3/\Gamma$ with $\Gamma=\Delta(3n^2)$ and $\Delta(6n^2)$, nonabelian finite subgroups of SU(3). We first construct a brane configuration for ${\bf C}^3/{\bf Z}_n \times {\bf Z}_n$ by using D3-branes and a web of (p,q) 5-branes of type IIB string theory. Brane configurations for the nonabelian orbifolds are obtained by performing certain quotients on the configuration for ${\bf C}^3/{\bf Z}_n \times {\bf Z}_n$. Structure of the quiver diagrams of the groups $\Delta(3n^2)$ and $\Delta(6n^2)$ can be reproduced from the brane configurations. We point out that the brane configuration for ${\bf C}^3/\Gamma$ can be regarded as a physical realization of the quiver diagram of $\Gamma$. Based on this observation, we discuss that three-dimensional McKay correspondence may be interpreted as T-duality.