## Abstract

We study toric singularities of the form of ℂ4/T for finite abelian groups Γ ⊂ SU(4). In particular, we consider the simplest case Γ = ℤ_{2} × ℤ_{2} × 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 × 2 × 2 brane cub model. We analyze geometric interpretation for field theory parameters and moduli space.

Original language | English |
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Pages (from-to) | XXII-24 |

Journal | Journal of High Energy Physics |

Volume | 3 |

Issue number | 4 |

State | Published - 1999 |

## Keywords

- D-branes
- Field theories in lower dimensions
- Superstrings and heterotic strings
- Supersymmetry and duality