Aspects of Six-Dimensional Flux Compactifications

In this thesis we investigate various aspects of ux compactications in six-dimensionalquantum eld theories. After introducing the internal geometries, i.e. the two-dimensionaltorus T2 and one of its orbifolds T2=Z2, we classify possible gauge backgroundsincluding continuous and discrete Wilson lines with emphasis on a non-vanishing uxdensity. An operator analogy with the quantum harmonic oscillator allows for an explicitderivation of the mode functions of charged elds and demonstrates the advantage of ourinterpretation of discrete Wilson lines in terms of localized fractional gauge uxes. Wethen derive a globally supersymmetric action which captures the D-term supersymmetrybreaking induced by the internal magnetic eld and reproduces the Landau level massspectrum of the charged four-dimensional degrees of freedom. In this context we showthat, even though supersymmetry is broken at the compactication scale, the inclusion ofthe whole tower of charged states leads to vanishing quantum corrections for the Wilsonline eective potential on T2. This result is supported by a symmetry breaking argumentin which the Wilson line appears as a Goldstone boson. After that, we additionallyinclude gravitational eects within a supergravity eective action of the lightest modesin four dimensions. The dynamics of the moduli elds arising after compactication canbe encoded in the setup of N = 1 supergravity augmented with anomaly cancellationby the Green-Schwarz mechanism. This leads to a non-trivial transformation behaviorfor two axion elds under gauge variations in the low-energy eective action. As anapplication, we discuss an SO(10) U(1) grand unied theory which uses the multiplicityof fermionic zero modes in the ux background to induce the number of mattergenerations. Finally, we investigate a novel mechanism for generating de Sitter vacuain N = 1 supergravity based on a ux-induced positive denite D-term potential. Theinclusion of a superpotential, leading to negative contributions in the energy density,allows a successful stabilization of all elds. Employing a general approach to decouplethe Goldstino from the rest of the fermions, we evaluate the masses of all light degreesof freedom explicitly