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**Building blocks for generalized heterotic/F-theory duality.**
*(English)*
Zbl 1308.81147

Summary: In this note we propose a generalization of heterotic/F-theory duality. We introduce a set of non-compact building blocks which we glue together to reach compact examples of generalized duality pairs. The F-theory building blocks consist of non-compact elliptically fibered Calabi-Yau fourfolds which also admit a \(K3\) fibration. The compact elliptic model obtained by gluing need not have a globally defined \(K3\) fibration. By replacing the \(K3\) fiber of each F-theory building block with a \(T^2\), we reach building blocks in a heterotic dual vacuum which includes a position dependent dilaton and three-form flux. These building blocks are glued together to reach a heterotic flux background. We argue that in these vacua, the gauge fields of the heterotic string become localized, and remain dynamical even when gravity decouples. This enables a heterotic dual for the hyperflux GUT breaking mechanism which has recently figured prominently in F-theory GUT models. We illustrate our general proposal with some explicit examples.

### MSC:

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

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

14D06 | Fibrations, degenerations in algebraic geometry |

81V22 | Unified quantum theories |

81V17 | Gravitational interaction in quantum theory |