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Geometric T-Duality
- From a physicists point of view T-duality is a relation connecting string theories on different spacetimes. Mathematically speaking, T-duality should be a symmetric relation on the space of toroidal string backgrounds. Such a background consists of: a smooth manifold M; a torus bundle E over M - the total space modelling spacetime; a Riemannian metric g on E - modelling the field of gravity; a U(1)-bundle gerbe G with connection over E - modelling the Kalb- Ramond field. But as of now no complete model for T-duality exists. The three most notable approaches for T-duality are given by the differential approaches by Buscher in the form of the Buscher rules and by Bouwknegt, Evslin and Mathai in the form of T-duality with H-flux on the one hand, and by the topological approach given by Bunke, Rumpf and Schick which is known as topological T-duality. In this thesis we combine these different approaches to form the first model for T-duality over complete geometric toroidal string backgrounds and we will introduce an example for this geometric T-duality inspired by the Hopf bundle.
Author: | Malte Arthur Kunath |
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URN: | urn:nbn:de:gbv:9-opus-61574 |
Title Additional (German): | Geometrische T-Dualität |
Referee: | Prof. Dr. Konrad Waldorf, Prof. Dr. Tilmann Wurzbacher |
Advisor: | Prof. Dr. Konrad Waldorf |
Document Type: | Doctoral Thesis |
Language: | English |
Year of Completion: | 2022 |
Granting Institution: | Universität Greifswald, Mathematisch-Naturwissenschaftliche Fakultät |
Date of final exam: | 2022/03/02 |
Release Date: | 2022/05/02 |
Tag: | Hopfbündel; T-Dualität Bundle gerbe; Buscher rules; Bündelgerbe; Hopf bundle; T-Duality |
GND Keyword: | Dualität, Differentialgeometrie, Kategorientheorie |
Page Number: | 85 |
Faculties: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik und Informatik |
DDC class: | 500 Naturwissenschaften und Mathematik / 510 Mathematik |