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Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 02/05 Podcast
Toroidal Orbifolds: Resolutions, Orientifolds and Applications in String Phenomenology

Toroidal Orbifolds: Resolutions, Orientifolds and Applications in String Phenomenology

Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 02/05 vor 20 Jahren

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As of now, string theory is the best candidate for a theory of
quantum gravity. Since it is anomaly–free only in ten space-time
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 non-Abelian 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
flux-induced 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, non-perturbative effects serve to stabilize all moduli. In
a second step, a meta-stable 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.