Compact F-theory GUTs with U(1)_PQ

We construct semi-local and global realizations of SU(5) GUTs in F-theory that utilize a U(1)_PQ symmetry to protect against dimension four proton decay. Symmetries of this type, which assign charges to H_u and H_d that forbid a tree level \mu term, play an important role in scenarios for neutrino physics and gauge mediation that have been proposed in local F-theory model building. As demonstrated in arXiv:0906.4672, the presence of such a symmetry implies the existence of non-GUT exotics in the spectrum, when hypercharge flux is used to break the GUT group and to give rise to doublet-triplet splitting. These exotics are of precisely the right type to solve the unification problem in such F-theory models and might also comprise a non-standard messenger sector for gauge mediation. We present a detailed description of models with U(1)_PQ in the semi-local regime, which does not depend on details of any specific Calabi-Yau four-fold, and then specialize to the geometry of arXiv:0904.3932 to construct three-generation examples with the minimal allowed number of non-GUT exotics. Among these, we find a handful of models in which the D3-tadpole constraint can be satisfied without requiring the introduction of anti-D3-branes. Finally, because SU(5) singlets that carry U(1)_PQ charge may serve as candidate right-handed neutrinos or can be used to lift the exotics, we study their origin in compact models and motivate a conjecture for how to count their zero modes in a semi-local setting.Comment: 73 pages, 5 figures, v2: minor corrections to 4.3 and 6.3.1, reference adde

G-flux and Spectral Divisors

We propose a construction of G-flux in singular elliptic Calabi-Yau fourfold compactifications of F-theory, which in the local limit allow a spectral cover description. The main tool of construction is the so-called spectral divisor in the resolved Calabi-Yau geometry, which in the local limit reduces to the Higgs bundle spectral cover. We exemplify the workings of this in the case of an E_6 singularity by constructing the resolved geometry, the spectral divisor and in the local limit, the spectral cover. The G-flux constructed with the spectral divisor is shown to be equivalent to the direct construction from suitably quantized linear combinations of holomorphic surfaces in the resolved geometry, and in the local limit reduces to the spectral cover flux.Comment: 30 page

Constitutive Heterochromatin in Eukaryotic Genomes: A Mine of Transposable Elements

Transposable elements (TEs) are abundant components of constitutive heterochromatin of the most diverse evolutionarily distant organisms. TEs enrichment in constitutive heterochromatin was originally described in the model organism Drosophila melanogaster, but it is now considered as a general feature of this peculiar portion of the genomes. The phenomenon of TE enrichment in constitutive heterochromatin has been proposed to be the consequence of a progressive accumulation of transposable elements caused by both reduced recombination and lack of functional genes in constitutive heterochromatin. However, this view does not take into account classical genetics studies and most recent evidence derived by genomic analyses of heterochromatin in Drosophila and other species. In particular, the lack of functional genes does not seem to be any more a general feature of heterochromatin. Sequencing and annotation of Drosophila melanogaster constitutive heterochromatin have shown that this peculiar genomic compartment contains hundreds of transcriptionally active genes, generally larger in size than that of euchromatic ones. Together, these genes occupy a significant fraction of the genomic territory of heterochromatin. Moreover, transposable elements have been suggested to drive the formation of heterochromatin by recruiting HP1 and repressive chromatin marks. In addition, there are several pieces of evidence that transposable elements accumulation in the heterochromatin might be important for centromere and telomere structure. Thus, there may be more complexity to the relationship between transposable elements and constitutive heterochromatin, in that different forces could drive the dynamic of this phenomenon. Among those forces, preferential transposition may be an important factor. In this article, we present an overview of experimental findings showing cases of transposon enrichment into the heterochromatin and their positive evolutionary interactions with an impact to host genomes

What Have We Learned in 30 Years of Investigations on Bari Transposons?

Transposable elements (TEs) have been historically depicted as detrimental genetic entities that selfishly aim at perpetuating themselves, invading genomes, and destroying genes. Scientists often co-opt “special” TEs to develop new and powerful genetic tools, that will hopefully aid in changing the future of the human being. However, many TEs are gentle, rarely unleash themselves to harm the genome, and bashfully contribute to generating diversity and novelty in the genomes they have colonized, yet they offer the opportunity to develop new molecular tools. In this review we summarize 30 years of research focused on the Bari transposons. Bari is a “normal” transposon family that has colonized the genomes of several Drosophila species and introduced genomic novelties in the melanogaster species. We discuss how these results have contributed to advance the field of TE research and what future studies can still add to the current knowledge

GUT theories from Calabi-Yau 4-folds with SO(10) Singularities

We consider an SO(10) GUT model from F-theory compactified on an elliptically fibered Calabi-Yau with a D5 singularity. To obtain the matter curves and the Yukawa couplings, we use a global description to resolve the singularity. We identify the vector and spinor matter representations and their Yukawa couplings and we explicitly build the G-fluxes in the global model and check the agreement with the semi-local results. As our bundle is of type SU(2k), some extra conditions need to be applied to match the fluxes.Comment: 27 page

Toric Construction of Global F-Theory GUTs

We systematically construct a large number of compact Calabi-Yau fourfolds which are suitable for F-theory model building. These elliptically fibered Calabi-Yaus are complete intersections of two hypersurfaces in a six dimensional ambient space. We first construct three-dimensional base manifolds that are hypersurfaces in a toric ambient space. We search for divisors which can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations over these base manifolds. We find that elementary conditions which are motivated by F-theory GUTs lead to strong constraints on the geometry, which significantly reduce the number of suitable models. The complete database of models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out several examples in more detail.Comment: 35 pages, references adde

Rational F-Theory GUTs without exotics

We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic phenomenology of the couplings places severe constraints on the allowed local models in a given geometry. In constructions based on the spectral cover we find no model satisfying all these requirements. We then provide a survey of models with additional U(1) symmetries arising from rational sections of the elliptic fibration in toric constructions and obtain phenomenologically appealing models based on SU(5) tops. Furthermore we perform a bottom-up exploration beyond the toric section constructions discussed in the literature so far and identify benchmark models passing all our criteria, which can serve as a guideline for future geometric engineering.Comment: 27 Pages, 1 Figur

A Global SU(5) F-theory model with Wilson line breaking

We engineer compact SU(5) Grand Unified Theories in F-theory in which GUT-breaking is achieved by a discrete Wilson line. Because the internal gauge field is flat, these models avoid the high scale threshold corrections associated with hypercharge flux. Along the way, we exemplify the `local-to-global' approach in F-theory model building and demonstrate how the Tate divisor formalism can be used to address several challenges of extending local models to global ones. These include in particular the construction of G-fluxes that extend non-inherited bundles and the engineering of U(1) symmetries. We go beyond chirality computations and determine the precise (charged) massless spectrum, finding exactly three families of quarks and leptons but excessive doublet and/or triplet pairs in the Higgs sector (depending on the example) and vector-like exotics descending from the adjoint of SU(5)_{GUT}. Understanding why vector-like pairs persist in the Higgs sector without an obvious symmetry to protect them may shed light on new solutions to the mu problem in F-theory GUTs.Comment: 95 pages (71 pages + 1 Appendix); v2 references added, minor correction

Building SO(10) models from F-theory

We revisit local F-theory SO(10) and SU(5) GUTs and analyze their properties within the framework of the maximal underlying E_8 symmetry in the elliptic fibration. We consider the symmetry enhancements along the intersections of seven-branes with the GUT surface and study in detail the embedding of the abelian factors undergoing monodromies in the covering gauge groups. We combine flux data from the successive breaking of SO(10) to SU(5) gauge symmetry and subsequently to the Standard Model one, and further constrain the parameters determining the models' particle spectra. In order to eliminate dangerous baryon number violating operators we propose ways to construct matter parity like symmetries from intrinsic geometric origin. We study implementations of the resulting constrained scenario in specific examples obtained for a variety of monodromies.Comment: 53 page