Branes at $\C^4/\Ga$ Singularity from Toric Geometry

Details Branes at $\C^4/\Ga$ Singularity from Toric Geometry Branes at $\C^4/\Ga$ Singularity from Toric Geometry

1999-03-22

arxiv.org/abs/hep-th/9903181v3

JHEP 9904 (1999) 012

Physics

High Energy Physics

High Energy Physics - Theory

1 figure, 4 tables, latex file and 26 pages:v1 added mathematical results on projective crepant resolutions by Dais et al and

Scientific paper

10.1088/1126-6708/1999/04/012

We study toric singularities of the form of $\C^4/\Ga$ for finite abelian groups $\Ga \subset SU(4)$. In particular, we consider the simplest case $\Ga=\Z_2 \times \Z_2 \times \Z_2$ and find explicitly charge matrices for partial resolutions of this orbifold by extending the method by Morrison and Plesser. We obtain three kinds of algebraic equations, $z_1 z_2 z_3 z_4=z_5^2, z_1 z_2 z_3=z_4^2 z_5 $ and $z_1 z_2 z_5 = z_3 z_4$ where $z_i$'s parametrize $\C^5$. When we put $N$ D1 branes at this singularity, it is known that the field theory on the worldvolume of $N$ D1 branes is T-dual to $2 \times 2 \times 2 $ brane cub model. We analyze geometric interpretation for field theory parameters and moduli space.

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