Kapfer, Andreas (2016): Geometric symmetries and topological terms in F-theory and field theory. Dissertation, LMU München: Faculty of Physics |

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**DOI**: 10.5282/edoc.19928

### Abstract

In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory. The first part treats settings of supersymmetry breaking in five dimensions. We focus on an N = 4 to N = 2 breaking in gauged supergravity. For certain classes of embedding tensors we can analyze the theory around the vacuum to a great extent. Importantly, one-loop corrections to Chern-Simons terms are generically induced which are independent of the supersymmetry-breaking scale. We investigate concrete examples of consistent truncations of supergravity and M-theory which show this N = 4 to N = 2 breaking pattern in five dimensions. In particular, we analyze necessary conditions for these consistent truncations to be used as effective theories for phenomenology by demanding consistency of the scale-independent corrections to Chern-Simons couplings. The second part is devoted to the study of anomalies and large gauge transformations in circle-reduced gauge theories and F-theory. We consider four- and six-dimensional matter-coupled gauge theories on the circle and classify all large gauge transformations that preserve the boundary conditions of the matter fields. Enforcing that they act consistently on one-loop Chern-Simons couplings in three and five dimensions explicitly yields all higher-dimensional gauge anomaly cancelation conditions. In the context of F-theory compactifications we identify the classified large gauge transformations along the circle with arithmetic structures on elliptically-fibered Calabi-Yau manifolds via the dual M-theory setting. Integer Abelian large gauge transformations correspond to free basis shifts in the Mordell-Weil lattice of rational sections while special fractional non-Abelian large gauge transformations are matched to torsional shifts in the Mordell-Weil group. For integer non-Abelian large gauge transformations we suggest a new geometric group structure on resolved elliptic fibrations. In the same way we also propose a novel group operation for multi-sections in genus-one fibrations without a proper section. We stress that these arithmetic structures ensure the cancelation of all gauge anomalies in F-theory compactifications on Calabi-Yau manifolds.

Item Type: | Theses (Dissertation, LMU Munich) |
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Subjects: | 500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics |

Faculties: | Faculty of Physics |

Language: | English |

Date of oral examination: | 6. October 2016 |

1. Referee: | Lüst, Dieter |

MD5 Checksum of the PDF-file: | c6c04cd795e7dcf4644840e72ad6c056 |

Signature of the printed copy: | 0001/UMC 24209 |

ID Code: | 19928 |

Deposited On: | 11. Nov 2016 08:35 |

Last Modified: | 23. Oct 2020 20:09 |