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

Changhyun Ahn; Hoil Kim

doi:10.1088/1126-6708/1999/04/012

paper

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

arXiv:hep-th/9903181 · doi:10.1088/1126-6708/1999/04/012

Abstract

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.

1 figure, 4 tables, latex file and 26 pages:v1 added mathematical results on projective crepant resolutions by Dais et al and refs added:v2 typos corrected and the beginning paragrphs in section 3 clarified

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

Abstract

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