Aspects of string theory compactifications: D-brane statistics and generalised geometry

Published: July 13, 2006, 11 a.m.

In this thesis two different aspects of string theory compactifications are investigated.\n\nThe first part deals with the issue of the huge\namount of possible string vacua, known as the landscape. Concretely\nwe investigate a specific well defined subset of type II orientifold\ncompactifications. We develop the necessary tools to construct a very\nlarge set of consistent models and investigate their gauge sector\non a statistical basis.\nIn particular we analyse the frequency distributions of gauge groups\nand the possible amount of chiral matter for compactifications to six and\nfour dimensions. In the phenomenologically relevant case of four-dimensional\ncompactifications, special attention is paid to solutions with gauge groups\nthat include those of the standard model, as well as Pati-Salam, SU(5) and\nflipped SU(5) models. Additionally we investigate the frequency distribution\nof coupling constants and correlations between the observables in the gauge\nsector. These results are compared with a recent study of Gepner\nmodels.\nMoreover, we elaborate on questions concerning the finiteness of the\nnumber of solutions and the computational complexity of the algorithm.\n\nIn the second part of this thesis we consider a new mathematical framework,\ncalled generalised geometry, to describe the six-manifolds used in\nstring theory compactifications. In particular, the formulation\nof T-duality and mirror symmetry for nonlinear topological sigma models\nis investigated.\nTherefore we provide a reformulation and extension of the known\ntopological A- and B-models to the generalised framework.\nThe action of mirror symmetry on topological D-branes in this setup is\npresented and the transformation of the boundary conditions is analysed.\nTo extend the considerations to D-branes in type II string theory, we\nintroduce the notion of generalised calibrations. We show that the known\ncalibration conditions of supersymmetric branes in type IIA and IIB can be\nobtained as special cases.\nFinally we investigate the action of T-duality on the generalised calibrations.