Reffert, Susanne / S. (2006): Toroidal Orbifolds: Resolutions, Orientifolds and Applications in String Phenomenology. Dissertation, LMU München: Faculty of Physics 

PDF
Reffert_Susanne.pdf 1594Kb 
Abstract
As of now, string theory is the best candidate for a theory of quantum gravity. Since it is anomaly–free only in ten spacetime dimensions, the six surplus spatial dimensions must be compactified. This thesis is concerned with the geometry of toroidal orbifolds and their applications in string theory. An orbifold is the quotient of a smooth manifold by a discrete group. In the present thesis, we restrict ourselves to orbifolds of the form T^6 /Z_N or T^6 /Z_N × Z_M . These so–called toroidal orbifolds are particularly popular as compactification manifolds in string theory. They present a good compromise between a trivial compactification manifold, such as the T^6 and one which is so complicated that explicit calculations are nearly impossible, which unfortunately is the case for many if not most Calabi–Yau manifolds. At the fixed points of the discrete group which is divided out, the orbifold develops quotient singularities. By resolving these singularities via blow–ups, one arrives at a smooth Calabi–Yau manifold. The systematic method to do so is explained in detail. Also the transition to the Orientifold quotient is explained. In string theory, toroidal orbifolds are popular because they combine the advantages of calculability and of incorporating many features of the standard model, such as nonAbelian gauge groups, chiral fermions and family repetition. In the second part of this thesis, applications in string phenomenology are discussed. The applications belong to the framework of compactifications with fluxes in type IIB string theory. Flux compactifications on the one hand provide a mechanism for supersymmetry breaking. One the other hand, they generically stabilize at least part of the geometric moduli. The geometric moduli, i.e. the deformation parameters of the compactification manifold correspond to massless scalar fields in the low energy effective theory. Since such massless fields are in conflict with experiment, mechanisms which generate a potential for them and like this fix the moduli to specific values must be investigated. After some preliminaries, two main examples are discussed. The first belongs to the category of model building, where concrete models with realistic properties are investigated. A brane model compactified on T^6 /Z_2 × Z_2 is discussed. The fluxinduced soft supersymmetry breakingparameters are worked out explicitly. The second example belongs to the sub ject of moduli stabilization along the lines of the proposal of Kachru, Kallosh, Linde and Trivedi (KKLT). Here, in addition to the background fluxes, nonperturbative effects serve to stabilize all moduli. In a second step, a metastable vacuum with a small positive cosmological constant is achieved. Orientifold models which result from resolutions of toroidal orbifolds are discussed as possible candidate models for an explicit realization of the KKLT proposal. The appendix collects the technical details for all commonly used toroidal orbifolds and constitutes a reference book for these models.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  String Theory, Flux Compactifications, Toroidal Orbifold, Orientifold, Toric Geometry 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  21. July 2006 
1. Referee:  Lüst, Dieter 
Persistent Identifier (URN):  urn:nbn:de:bvb:1957651 
MD5 Checksum of the PDFfile:  4d2e0a4fa22436ab2c34ae52496d07cd 
Signature of the printed copy:  0001/UMC 15609 
ID Code:  5765 
Deposited On:  28. Aug 2006 
Last Modified:  16. Oct 2012 08:00 