Evidence for F-theory.

*(English)*Zbl 1003.81531Summary: We construct compact examples of \(D\)-manifolds for type IIB strings. The construction has a natural interpretation in terms of compactification of a 12-dimensional F-theory. We provide evidence for a more natural reformulation of type IIB theory in terms of F-theory. Compactification of M-theory on a manifold \(K\) which admits elliptic fibration is equivalent to compactification of \(F\)-theory on \(K\times S^{1}\). A large class of \(N=1\) theories in 6 dimensions are obtained by compactification of F-theory on Calabi-Yau threefolds. A class of phenomenologically promising compactifications of \(F\)-theory is on Spin(7) holonomy manifolds down to 4 dimensions. This may provide a concrete realization of Witten’s proposal for solving the cosmological constant problem in four dimensions.

##### MSC:

81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |

14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |

32J17 | Compact complex \(3\)-folds |

32J81 | Applications of compact analytic spaces to the sciences |

83E30 | String and superstring theories in gravitational theory |

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