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Gauge Theories and Geometry in Non-Perturbative String Theory

Student thesis: Doctoral ThesisDoctor of Philosophy

The central theme in this thesis is compactifications: reductions of higher dimensional theories to lower dimensions and how the geometry of the compactification manifold determines features of the low energy physics. This is studied in the context of non-perturbative string theory in the framework of M-theory and F-theory.
Supersymmetry requires the compactification manifold in F-theory to be an elliptically fibered Calabi-Yau, where the complex structure of the elliptic fibration is identified with the complexified coupling constant in type IIB string theory. The non-perturbative nature of the theory originates from the strong-weak duality of type IIB, which manifests itself as the SL(2;Z) modular transformation of the complex structure. Non-abelian gauge symmetries arise naturally in this framework and engineering Grand Uni ed Theories within F-theory has been an active area of research. Compactifications on Calabi-Yau four-folds give rise to gauge theories with N = 1 supersymmetry in four dimensions coupled to gravity. In the first part of this thesis we focus on abelian gauge symmetries in F-theory, which are essential in SU(5) GUTs for forbidding couplings which result in fast proton decay. These arise from rational sections in the elliptic fibration and from the geometric constraints on these sections one can determine the set of possible U(1) charges of GUT matter representations. Armed with this constrained set of charges we then proceed to study the phenomenology of these abelian gauge symmetries in the context of SU(5) GUT models. We analyse their e ectiveness at suppressing proton decay operators and explore the types of realistic flavour textures that can be generated using the Froggatt-Nielsen mechanism.
In the latter part of this thesis the focal point changes to M5-branes, one of the two fundamental objects of M-theory. The theory of multiple M5-branes is known to be a 6d N = (2; 0) superconformal eld theory, of which only the space-time symmetries and abelian equations of motion have been determined. In spite of this, fascinating correspondences have been shown to arise from the reduction of the M5-brane theory to lower dimensions. In particular, supersymmetric observables in the reduced theories capture non-trivial aspects of the geometry of the compactification manifold. The final chapter of this thesis studies the compactification of the 6d N = (2; 0) theory on the two-sphere as a step towards deriving a correspondence related to four-manifolds.
Original languageEnglish
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Award date2017

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