arXiv subjects
Publications and source records attributed to S. Reffert.
These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is wholly on the geometry side, not on the physics. The treated topics include toroidal orbifolds, methods of toric geometry, desinglularization of toroidal orbifolds and their orientifold quotients.
We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi-Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.
We discuss general properties of moduli stablization in KKLT scenarios in type IIB orientifold compactifications. In particular, we find conditions for the Kaehler potential to allow a KKLT scenario for a manifold X_6 without complex structure moduli, i.e. h_(2,1)(X_6)=0. This way, a whole class of type IIB orientifolds with h_(2,1)(X_6)=0 is ruled out. This excludes in particular all Z_N- and Z_N x Z_M-orientifolds X_6 with h_(2,1)(X_6)=0 for a KKLT scenario. This concerns Z_3, Z_7, Z_3 x Z_3, Z_4 x Z_4, Z_6 x Z_6 and Z_2 x Z_6' -both at the orbifold point and away from it. Furthermore, we propose a mechanism to stabilize the Kaehler moduli accociated to the odd cohomology H^(1,1)_-(X_6). In the second part of this work we discuss the moduli stabilization of resolved type IIB Z_N- or Z_N x Z_M - orbifold/orientifold compactifications. As examples for the resolved Z_6 and Z_2 x Z_4 orbifolds we fix all moduli through a combination of fluxes and racetrack superpotential.
We discuss flux quantization and moduli stabilization in toroidal type IIB Z_N - or Z_N x Z_M -orientifolds, focusing mainly on their orbifold limits. After presenting a detailed discussion of their moduli spaces and effective actions, we study the supersymmetric vacuum structure of these models and derive criteria for the existence of stable minima. Furthermore, we briefly investigate the models away from their orbifold points and comment on the microscopic origin of their non-perturbative superpotentials.
This thesis is concerned with the geometry of toroidal orbifolds and their applications in string theory. By resolving the orbifold 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 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. The first example belongs to the category of model building, flux-induced soft supersymmetry breaking parameters are worked out explicitly. The second example belongs to the subject of moduli stabilization along the lines of the KKLT proposal. Orientifold models which result from resolutions of toroidal orbifolds are discussed as possible candidate models for an explicit realization of the KKLT proposal.
Context: Future astrometric missions such as SIM PlanetQuest need very stable reference stars. K giants have large luminosities, which place them at large distances and thus the jitter of their photocenters by companions is relatively small. Therefore K giants would be best suited as references. To confirm this observationally a radial velocity survey is performed to quantify the level of intrinsic variability in K giants. Aims: From this radial velocity survey we present 34 K giants with an observed standard deviation of the radial velocity of less than 20 m/s. These stars are considered ``stable'' and can be used as radial velocity standards. Methods: The radial velocity survey contains 179 K giants. All K giants have a declination between -30 and +65 degrees and visual magnitude of 3-6 mag. The Coude Auxiliary Telescope (CAT) at UCO/Lick Observatory is used to obtain radial velocities with an accuracy of 5-8 m/s. The number of epochs for the 34 stable stars ranges from 11 to 28 with a total timespan of the observations between 1800 and a little over 2200 days. Results: The observational results of the 34 ``stable'' stars are shown together with a discussion about their position in the M_{V} vs. B-V diagram and some conclusions concerning the radial velocity variability of K giants. These results are in agreement with the theoretical predictions. K giants in a certain range of the M_{V} vs. B-V diagram are suitable reference stars.
We discuss the structure of the soft supersymmetry breaking terms in a MSSM like model, which can be derived from D7-branes with chiral matter fields from 2-form f-fluxes and supersymmetry breaking from 3-form G-fluxes.
We use F-theory to derive a general expression for the flux potential of type II compactifications with D7/D3 branes, including open string moduli and 2-form fluxes on the branes. Our main example is F-theory on K3 $\times$ K3 and its orientifold limit T^2/Z_2 x K3. The full scalar potential cannot be derived from the bulk superpotential W=\int Ω\wedge G_3 and generically destabilizes the orientifold. Generically all open and closed string moduli are fixed, except for a volume factor. An alternative formulation of the problem in terms of the effective supergravity is given and we construct an explicit map between the F-theory fluxes and gaugings. We use the superpotential to compute the effective action for flux compactifications on orbifolds, including the μ-term and soft-breaking terms on the D7-brane world-volume.
We present results of an investigation of the X-ray properties, age distribution, and kinematical characteristics of a high-galactic latitude sample of late-type field stars selected from the ROSAT All-Sky Survey (RASS). The sample comprises 254 RASS sources with optical counterparts of spectral types F to M distributed over six study areas located at |b| >= 20 degr, and DEC >= -9 degr. A detailed study was carried out for the subsample of ~200 G, K, and M stars. Lithium abundances were determined for 179 G-M stars. Radial velocities were measured for most of the 141 G and K type stars of the sample. Combined with proper motions these data were used to study the age distribution and the kinematical properties of the sample. Based on the lithium abundances half of the G-K stars were found to be younger than the Hyades (660 Myr). About 25% are comparable in age to the Pleiades (100 Myr). A small subsample of 10 stars is younger than the Pleiades. They are therefore most likely pre-main sequence stars. Kinematically the PMS and Pleiades-type stars appear to form a group with space velocities close to the Castor moving group but clearly distinct from the Local Association.
We discuss supersymmetry breaking via 3-form fluxes in chiral supersymmetric type IIB orientifold vacua with D3- and D7-branes. After a general discussion of possible choices of fluxes allowing for stabilizing of a part of the moduli, we determine the resulting effective action including all soft supersymmetry breaking terms. We also extend the computation of our previous work concerning the matter field metrics arising from various open string sectors, in particular focusing on the 1/2 BPS D3/D7-brane configuration. Afterwards, the F-theory lift of our constructions is investigated.