Ralph Blumenhagen

Noncommutative compactifications of type I strings on tori with magnetic background flux

Weconstructsix-andfour-dimensionaltoroidalcompacticationsofthe type-IstringwithmagneticfluxontheD-branes. Theopenstringsinthisbackground probe a noncommutative internal geometry. Phenomenologically appealing features suchaschiralfermionsandsupersymmetrybreakinginthegaugesectorarenaturally realized by these vacua. We investigate the spectra of such noncommutative string compactications and in a bottom-up approach discuss the possibility to obtain the standard or some GUT like model.

The Standard Model from stable intersecting brane world orbifolds

Abstract We analyze the perturbative stability of non-supersymmetric intersecting brane world models on tori. Besides the dilaton tadpole, a dynamical instability in the complex structure moduli space occurs at string disc level, which drives the background geometry to a degenerate limit. We show that in certain orbifold models this latter instability is absent as the relevant moduli are frozen. We construct explicit examples of such orbifold intersecting brane world models and discuss the phenomenological implications of a three generation Standard Model which descends naturally from an SU (5) GUT theory. It turns out that various phenomenological issues require the string scale to be at least of the order of the GUT scale. As a major difference compared to the Standard Model, some of the Yukawa couplings are excluded so that the standard electroweak Higgs mechanism with a fundamental Higgs scalar is not realized in this set-up.

Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes

We investigate orientifolds of type II string theory on K3 and Calabi-Yau 3-folds with intersecting D-branes wrapping special lagrangian cycles. We determine quite generically the chiral massless spectrum in terms of topological invariants and discuss both orbifold examples and algebraic realizations in detail. Intriguingly, the developed techniques provide an elegant way to figure out the chiral sector of orientifold models without computing any explicit string partition function. As a new example we derive a non-supersymmetric Standard-like Model from an orientifold of type IIA on the quintic Calabi-Yau 3-fold with wrapped D6-branes. In the case of supersymmetric intersecting brane models on Calabi-Yau manifolds we discuss the D-term and F-term potentials, the effective gauge couplings and the Green-Schwarz mechanism. The mirror symmetric formulation of this construction is provided within type IIB theory. We finally include a short discussion about the lift of these models from type IIB on K3 to F-theory and from type IIA on Calabi-Yau 3-folds to M-theory on G2 manifolds.

Type I strings with F- and B-flux

We present non-supersymmetric toroidal compactifications of type-I string theory with both constant background NSNS two-form flux and non-trivial magnetic flux on the various D9-branes. The non-vanishing B-flux admits four-dimensional models with three generations of chiral fermions in standard model like gauge groups. Additionally, we consider the orbifold 4/2, again with both kinds of background flux present, leading to non-supersymmetric as well as supersymmetric models in six dimensions. All models have T-dual descriptions as intersecting brane worlds.

Moduli stabilization in chiral type IIB orientifold models with fluxes

Abstract We consider type IIB orientifold models on Calabi–Yau spaces with three-form G-flux turned on. These fluxes freeze some of the complex structure moduli and the complex dilaton via an F-term scalar potential. By introducing pairs of D9– D9 branes with Abelian magnetic fluxes it is possible to freeze also some of the Kahler moduli via a D-term potential. Moreover, such magnetic fluxes in general lead to chiral fermions, which make them interesting for string model-building. These issues are demonstrated in a simple toy model based on a Z 2 × Z 2 ′ orbifold.

Supersymmetric Intersecting Branes on the Type IIA T6/Bbb Z4 Orientifold

We study supersymmetric intersecting D6-branes wrapping 3-cycles in the type-IIA T6/4 orientifold background. As a new feature, the 3-cycles in this orbifold space arise both from the untwisted and the 2 twisted sectors. We present an integral basis for the homology lattice, H3(M,), in terms of fractional 3-cycles, for which the intersection form involves the Cartan matrix of E8. We show that these fractional D6-branes can be used to construct supersymmetric brane configurations realizing a three generation Pati-Salam model. Via brane recombination processes preserving supersymmetry, this GUT model can be broken down to a standard-like model.

Gauge unification in supersymmetric intersecting brane worlds

We show that contrary to first expectations realistic three generation supersymmetric intersecting brane world models give rise to phenomenologically interesting predictions about gauge coupling unification. Assuming the most economical way of realizing the matter content of the MSSM via intersecting branes we obtain a model independent relation among the three gauge coupling constants at the string scale. In order to correctly reproduce the experimentally known values of sin 2θw(Mz) and αs(Mz) this relation leads to natural gauge coupling unification at a string scale close to the standard GUT scale 2 × 1016 GeV. Additional vector-like matter can push the unification scale up to the Planck scale.

Supersymmetric orientifolds in 6D with D-branes at angles

Abstract We study a new class of N=1 supersymmetric orientifolds in six space-time dimensions. The world-sheet parity transformation is combined with a permutation of the internal complex coordinates. In contrast to ordinary orientifolds the twisted sectors contribute to the Klein bottle amplitude leading to new tadpoles to be cancelled by twisted open string sectors. They arise from open strings stretched between D7-branes intersecting at non-trivial angles. We study in detail the Z 3 , Z 4 and Z 6 permutational orientifolds obtaining in all cases anomaly free massless spectra.

Hybrid Inflation in Intersecting Brane Worlds

Abstract Non-supersymmetric brane world scenarios in string theory display perturbative instabilities that usually involve run-away potentials for scalar moduli fields. We investigate in the framework of intersecting brane worlds whether the leading order scalar potential for the closed string moduli allows to satisfy the slow-rolling conditions required for applications in inflationary cosmology. Adopting a particular choice of basis in field space and assuming mechanisms to stabilize some of the scalars, we find that slow-rolling conditions can be met very generically. In intersecting brane worlds inflation can end nearly instantaneously like in the hybrid inflation scenario due to the appearance of open string tachyons localized at the intersection of two branes, which signal a corresponding phase transition in the gauge theory via the condensation of a Higgs field.

Asymmetric orbifolds, noncommutative geometry and type I string vacua

Abstract We investigate the D-brane contents of asymmetric orbifolds. Using T-duality we find that the consistent description of open strings in asymmetric orbifolds requires to turn on background gauge fields on the D-branes. We derive the corresponding noncommutative geometry arising on such D-branes with mixed Neumann–Dirichlet boundary conditions directly by applying an asymmetric rotation to open strings with pure Dirichlet or Neumann boundary conditions. As a concrete application of our results we construct asymmetric type I vacua requiring open strings with mixed boundary conditions for tadpole cancellation.