Abstract:We construct a set of chirality inducing G 4 -fluxes in global F-theory compactifications on Calabi-Yau four-folds. Special emphasis is put on models with gauge group SU (5) × U (1) X relevant in the context of F-theory GUT model building, which are described in terms of a U (1)-restricted Tate model. A G 4 -flux arises in a manner completely analogous to the U (1) X gauge potential. We describe in detail the resolution by blow-up of the various singularities responsible for the U (1) X factor and the standard SU (5) gauge group and match the result with techniques applied in the context of toric geometry. This provides an explicit identification of the structure of the resolved fibre over the matter curves and over the enhancement points relevant for Yukawa couplings. We compute the flux-induced chiral index both of SU (5) charged matter and of SU (5) singlets charged only under U (1) X localised on curves which are not contained in the SU (5) locus. We furthermore discuss global consistency conditions such as D3-tadpole cancellation, D-term supersymmetry and Freed-Witten quantisation. The U (1) X gauge flux is a global extension of a class of split spectral cover bundles. It constitutes an essential ingredient in the construction of globally defined F-theory compactifications with chiral matter. We exemplify this in a three-generation SU (5) × U (1) X model whose flux satisfies all of the above global consistency conditions. We also extend our results to chiral fluxes in models without U (1) restriction.arXiv:1109.3454v2 [hep-th]

In the context of type IIB string theory we combine moduli stabilisation and model building on branes at del Pezzo singularities in a fully consistent global compactification. By means of toric geometry, we classify all the Calabi-Yau manifolds with 3 < h 1,1 < 6 which admit two identical del Pezzo singularities mapped into each other under the orientifold involution. This effective singularity hosts the visible sector containing the Standard Model while the Kähler moduli are stabilised via a combination of D-terms, perturbative and non-perturbative effects supported on hidden sectors.We present concrete models where the visible sector, containing the Standard Model, gauge and matter content, is built via fractional D3-branes at del Pezzo singularities and all the Kähler moduli are fixed providing an explicit realisation of both KKLT and LARGE volume scenarios, the latter with D-term uplifting to de Sitter minima.We perform the consistency checks for global embedding such as tadpole, K-theory charges and Freed-Witten anomaly cancellation. We briefly discuss phenomenological and cosmological implications of our models.

We present a systematic construction of F-theory compactifications with Abelian gauge symmetries in addition to a non-Abelian gauge group G. The formalism is generally applicable to models in global Tate form but we focus on the phenomenologically interesting case of G = SU(5). The Abelian gauge factors arise due to extra global sections resulting from a specific factorisation of the Tate polynomial which describes the elliptic fibration. These constructions, which accommodate up to four different U(1) factors, are worked out in detail for the two possible embeddings of a single U(1) factor into E 8 , usually denoted SU(5) × U(1) X and SU(5) × U(1) P Q . The resolved models can be understood either patchwise via a small resolution or in terms of a P 1,1,2 [4] description of the elliptic fibration. We derive the U(1) charges of the fields from the geometry, construct the U(1) gauge fluxes and exemplify the structure of the Yukawa interaction points. A particularly interesting result is that the global SU(5) × U(1) P Q model exhibits extra SU(5)-singlet states which are incompatible with a single global decomposition of the 248 of E 8 . The states in turn lead to new Yukawa type couplings which have not been considered in local model building.

Abstract:We provide a detailed correspondence between G 4 gauge fluxes in F-theory compactifications with SU (n) and SU (n) × U (1) gauge symmetry and their Type IIB orientifold limit. Based on the resolution of the relevant F-theory Tate models, we classify the factorisable G 4 -fluxes and match them with the set of universal D5-tadpole free U (1)-fluxes in Type IIB. Where available, the global version of the universal spectral cover flux corresponds to Type IIB gauge flux associated with a massive diagonal U (1). In U (1)-restricted Tate models extra massless abelian fluxes exist which are associated with specific linear combinations of Type IIB fluxes. Key to a quantitative match between F-theory and Type IIB is a proper treatment of the conifold singularity encountered in the Sen limit of generic F-theory models. We also shed further light on the brane recombination process relating generic and U (1)-restricted Tate models.

Abstract:We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kähler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content or some close extensions. In order to control complex structure moduli stabilisation we consider CalabiYau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kähler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative α ′ corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP 6 singularity which can be higgsed to the phenomenologically interesting class of models at the dP 3 singularity.