Volker Braun

GUTs in type IIB orientifold compactifications

Abstract We systematically analyse globally consistent SU ( 5 ) GUT models on intersecting D7-branes in genuine Calabi–Yau orientifolds with O3- and O7-planes. Beyond the well-known tadpole and K-theory cancellation conditions there exist a number of additional subtle but quite restrictive constraints. For the realisation of SU ( 5 ) GUTs with gauge symmetry breaking via U ( 1 ) Y flux we present two classes of suitable Calabi–Yau manifolds defined via del Pezzo transitions of the elliptically fibred hypersurface P 1 , 1 , 1 , 6 , 9 [ 18 ] and of the Quintic P 1 , 1 , 1 , 1 , 1 [ 5 ] , respectively. To define an orientifold projection we classify all involutions on del Pezzo surfaces. We work out the model building prospects of these geometries and present five globally consistent string GUT models in detail, including a 3-generation SU ( 5 ) model with no exotics whatsoever. We also realise other phenomenological features such as the 10 10 5 H Yukawa coupling and comment on the possibility of moduli stabilisation, where we find an entire new set of so-called swiss-cheese type Calabi–Yau manifolds. It is expected that both the general constrained structure and the concrete models lift to F-theory vacua on compact Calabi–Yau fourfolds.

New Global F-theory GUTs with U(1) symmetries

A bstractWe construct global F-theory GUTs with SU(5) × U(1) gauge group defined by specifying a fully resolved Calabi-Yau fourfold and consistent four-form G-flux. Its specific U(1) charged matter spectrum allows the desired Yukawa couplings, but forbids dangerous proton decay operators. The model we find: (1) does not follow from an underlying higgsed E8 gauge group (2) leaves the class of theories that can be analyzed with current splitspectral cover techniques. This avoids recently proposed no-go theorems for models with hypercharge flux, as required to break the GUT group. The appearance of additional fields is related geometrically to considering a more general class of sections and 4–1 splits. We show explicitly that the four-dimensional chiral matter index can still be computed using three-dimensional one-loop Chern-Simons terms.

On free quotients of complete intersection Calabi-Yau manifolds

In order to find novel examples of non-simply connected Calabi-Yau threefolds, free quotients of complete intersections in products of projective spaces are classified by means of a computer search. More precisely, all automorphisms of the product of projective spaces that descend to a free action on the Calabi-Yau manifold are identified.

A three‐generation Calabi‐Yau manifold with small Hodge numbers

We present a complete intersection Calabi-Yau manifold Y that has Euler number -72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group ℤ12 and the non-Abelian dicyclic group Dic3. The quotient manifolds have χ = -6 and Hodge numbers (h11, h21) = (1,4). With the standard embedding of the spin connection in the gauge group, Y gives rise to an E6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field. For the non-Abelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with (h11, h21) = (2,2) that lies right at the tip of the distribution of Calabi-Yau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in a toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev.

Toric Elliptic Fibrations and F-Theory Compactifications

A bstractThe 102,581 flat toric elliptic fibrations over

Stabilizing all Kähler moduli in type IIB orientifolds

{{mathbb{P}}^2}

The MSSM Spectrum from (0,2)-Deformations of the Heterotic Standard Embedding

are identified among the Calabi-Yau hypersurfaces that arise from the 473,800,776 reflexive 4-dimensional polytopes. In order to analyze their elliptic fibration structure, we describe the precise relation between the lattice polytope and the elliptic fibration. The fiber-divisor-graph is introduced as a way to visualize the embedding of the Kodaira fibers in the ambient toric fiber. In particular in the case of non-split discriminant components, this description is far more accurate than previous studies. The discriminant locus and Kodaira fibers of all 102,581 elliptic fibrations are computed. The maximal gauge group is SU(27), which would naively be in contradiction with 6-dimensional anomaly cancellation.

Global embeddings for branes at toric singularities

We describe a simple and robust mechanism that stabilizes all Kähler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G2 compactifications of M theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kähler moduli are worked out. We find that the stabilized volumes of all two-and four-cycles as well as the volume of the Calabi-Yau manifold are controlled by a single parameter, namely, the volume of the ample divisor. This feature would dramatically constrain any realistic models of particle physics embedded into such compactifications. Broad consequences for phenomenology are discussed, in particular the dynamical solution to the strong CP-problem within the framework.

Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories

A bstractWe construct supersymmetric compactifications of E8×E8 heterotic string theory which realise exactly the massless spectrum of the Minimal Supersymmetric Standard Model (MSSM) at low energies. The starting point is the standard embedding on a Calabi-Yau threefold which has Hodge numbers (h1,1, h2,1) = (1, 4) and fundamental group

The 24-Cell and Calabi-Yau Threefolds with Hodge Numbers (1,1)

{mathbb{Z}_{{12}}}