### Abstract

We construct the non-compact Calabi-Yau manifolds interpreted as the complex line bundles over the Hermitian symmetric spaces. These manifolds are the various generalizations of the complex line bundle over CP^{N-1}. Imposing an F-term constraint on the line bundle over CP^{N-1}, we obtain the line bundle over the complex quadric surface Q^{N-2}. On the other hand, when we promote the U (1) gauge symmetry in CP^{N-1} to the non-abelian gauge group U (M), the line bundle over the Grassmann manifold is obtained. We construct the non-compact Calabi-Yau manifolds with isometries of exceptional groups, which we have not discussed in the previous papers. Each of these manifolds contains the resolution parameter which controls the size of the base manifold, and the conical singularity appears when the parameter vanishes.

Original language | English |
---|---|

Pages (from-to) | 347-370 |

Number of pages | 24 |

Journal | Annals of Physics |

Volume | 296 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 Mar 15 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*296*(2), 347-370. https://doi.org/10.1006/aphy.2002.6226

**Gauge theoretical construction of non-compact Calabi-Yau manifolds.** / Higashijima, Kiyoshi; Kimura, Tetsuji; Nitta, Muneto.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 296, no. 2, pp. 347-370. https://doi.org/10.1006/aphy.2002.6226

}

TY - JOUR

T1 - Gauge theoretical construction of non-compact Calabi-Yau manifolds

AU - Higashijima, Kiyoshi

AU - Kimura, Tetsuji

AU - Nitta, Muneto

PY - 2002/3/15

Y1 - 2002/3/15

N2 - We construct the non-compact Calabi-Yau manifolds interpreted as the complex line bundles over the Hermitian symmetric spaces. These manifolds are the various generalizations of the complex line bundle over CPN-1. Imposing an F-term constraint on the line bundle over CPN-1, we obtain the line bundle over the complex quadric surface QN-2. On the other hand, when we promote the U (1) gauge symmetry in CPN-1 to the non-abelian gauge group U (M), the line bundle over the Grassmann manifold is obtained. We construct the non-compact Calabi-Yau manifolds with isometries of exceptional groups, which we have not discussed in the previous papers. Each of these manifolds contains the resolution parameter which controls the size of the base manifold, and the conical singularity appears when the parameter vanishes.

AB - We construct the non-compact Calabi-Yau manifolds interpreted as the complex line bundles over the Hermitian symmetric spaces. These manifolds are the various generalizations of the complex line bundle over CPN-1. Imposing an F-term constraint on the line bundle over CPN-1, we obtain the line bundle over the complex quadric surface QN-2. On the other hand, when we promote the U (1) gauge symmetry in CPN-1 to the non-abelian gauge group U (M), the line bundle over the Grassmann manifold is obtained. We construct the non-compact Calabi-Yau manifolds with isometries of exceptional groups, which we have not discussed in the previous papers. Each of these manifolds contains the resolution parameter which controls the size of the base manifold, and the conical singularity appears when the parameter vanishes.

UR - http://www.scopus.com/inward/record.url?scp=0037088336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037088336&partnerID=8YFLogxK

U2 - 10.1006/aphy.2002.6226

DO - 10.1006/aphy.2002.6226

M3 - Article

VL - 296

SP - 347

EP - 370

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 2

ER -