Brane Configurations for Three-dimensional Nonabelian Orbifolds

Abstract

We study brane configurations corresponding to D-branes on complex three-dimensional orbifolds ${\mathbf{C}}^3/\Gamma$ with $\Gamma =\Delta (3n^2)$ and $\Delta (6n^2)$, nonabelian finite subgroups of SU(3). We first construct a brane configuration for ${\mathbf{C}}^3/{\mathbf{Z}}_n\times {\mathbf{Z}}_n$ 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 ${\mathbf{C}}^3/{\mathbf{Z}}_n\times {\mathbf{Z}}_n$. 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 ${\mathbf{C}}^3/\Gamma$ 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.

22 pages, 12 figures, T-duality interpretation of the McKay correspondence added