Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-05-31
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, 12 figures, T-duality interpretation of the McKay correspondence added
Scientific paper
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.
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