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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.

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Author: Malte Arthur Kunath
Title Additional (German):Geometrische T-Dualität
Referee:Prof. Dr. Konrad Waldorf, Prof. Dr. Tilmann Wurzbacher
Advisor:Prof. Dr. Konrad Waldorf
Document Type:Doctoral Thesis
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