## Abstract

We investigate strings at singularities of G_{2}-holonomy manifolds which arise in Z{double-struck}_{2} orbifolds of Calabi-Yau spaces times a circle. The singularities locally look like R^{4}/Z{double-struck}_{2} fibered over a SLAG, and can globally be embedded in CICYs in weighted projective spaces. The local model depends on the choice of a discrete torsion in the fibration, and the global model on an anti-holomorphic involution of the Calabi-Yau hypersurface. We determine how these choices are related to each other by computing a Wilson surface detecting discrete torsion. We then follow the same orbifolds to the non-geometric Landau-Ginzburg region of moduli space. We argue that the symmetry-breaking twisted sectors are effectively captured by real Landau-Ginzburg potentials. In particular, we find agreement in the low-energy spectra of strings computed from geometry and Gepner-model CFT. Along the way, we construct the full modular data of orbifolds of J\f = 2 minimal models by the mirror automorphism, and give a real-LG interpretation of their modular invariants. Some of the models provide examples of the mirror-symmetry phenomenon for G_{2} holonomy.

Original language | English (US) |
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Pages (from-to) | 207-278 |

Number of pages | 72 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 6 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2002 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)