No abstract

We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E 8 × E 8 heterotic superstring on a smooth Calabi-Yau threefold with an SU(4) gauge instanton and a Z 3 × Z 3 Wilson line. Specifically, the observable sector is N = 1 supersymmetric with gauge groupthree families of quarks and leptons, each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair. Importantly, there are no extra vector-like pairs and no exotic matter in the zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge instanton moduli in the observable sector. The holomorphic SU(4) vector bundle of the observable sector is slope-stable.

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.

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 G 2 manifolds. 06/2002

We argue that M-theory compactified on an arbitrary genus-one fibration, that is, an elliptic fibration which need not have a section, always has an F-theory limit when the area of the genus-one fiber approaches zero. Such genus-one fibrations can be easily constructed as toric hypersurfaces, and various SU(5) × U(1) n and E 6 models are presented as examples. To each genus-one fibration one can associate a τ -function on the base as well as an SL(2, Z) representation which together define the IIB axio-dilaton and 7-brane content of the theory. The set of genus-one fibrations with the same τ -function and SL(2, Z) representation, known as the Tate-Shafarevich group, supplies an important degree of freedom in the corresponding F-theory model which has not been studied carefully until now.Six-dimensional anomaly cancellation as well as Witten's zero-mode count on wrapped branes both imply corrections to the usual F-theory dictionary for some of these models. In particular, neutral hypermultiplets which are localized at codimension-two fibers can arise. (All previous known examples of localized hypermultiplets were charged under the gauge group of the theory.) Finally, in the absence of a section some novel monodromies of Kodaira fibers are allowed which lead to new breaking patterns of non-Abelian gauge groups.