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

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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 Ftheory. 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, oneloop corrections to ChernSimons terms are generically induced which are independent of the supersymmetrybreaking scale. We investigate concrete examples of consistent truncations of supergravity and Mtheory 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 scaleindependent corrections to ChernSimons couplings. The second part is devoted to the study of anomalies and large gauge transformations in circlereduced gauge theories and Ftheory. We consider four and sixdimensional mattercoupled 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 oneloop ChernSimons couplings in three and five dimensions explicitly yields all higherdimensional gauge anomaly cancelation conditions. In the context of Ftheory compactifications we identify the classified large gauge transformations along the circle with arithmetic structures on ellipticallyfibered CalabiYau manifolds via the dual Mtheory setting. Integer Abelian large gauge transformations correspond to free basis shifts in the MordellWeil lattice of rational sections while special fractional nonAbelian large gauge transformations are matched to torsional shifts in the MordellWeil group. For integer nonAbelian 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 multisections in genusone fibrations without a proper section. We stress that these arithmetic structures ensure the cancelation of all gauge anomalies in Ftheory compactifications on CalabiYau manifolds.
Item Type:  Thesis (Dissertation, LMU Munich) 

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 PDFfile:  c6c04cd795e7dcf4644840e72ad6c056 
Signature of the printed copy:  0001/UMC 24209 
ID Code:  19928 
Deposited On:  11. Nov 2016 08:35 
Last Modified:  11. Nov 2016 08:35 