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

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

Thermal Evolution of the Non Supersymmetric Metastable Vacua in N=2 SU(2) SYM Softly Broken to N=1

It has been shown that four dimensional N=2 gauge theories, softly broken to N=1 by a superpotential term, can accommodate metastable non-supersymmetric vacua in their moduli space. We study the SU(2) theory at high temperatures in order to determine whether a cooling universe settles in the metastable vacuum at zero temperature. We show that the corrections to the free energy because of the BPS dyons are such that may destroy the existence of the metastable vacuum at high temperatures. Nevertheless we demonstrate the universe can settle in the metastable vacuum, provided that the following two conditions are hold: first the superpotential term is not arbitrarily small in comparison to the strong coupling scale of the gauge theory, and second the metastable vacuum lies in the strongly coupled region of the moduli space.Comment: 32 pages, 30 figure

Tate Form and Weak Coupling Limits in F-theory

We consider the weak coupling limit of F-theory in the presence of non-Abelian gauge groups implemented using the traditional ansatz coming from Tate's algorithm. We classify the types of singularities that could appear in the weak coupling limit and explain their resolution. In particular, the weak coupling limit of SU(n) gauge groups leads to an orientifold theory which suffers from conifold singulaties that do not admit a crepant resolution compatible with the orientifold involution. We present a simple resolution to this problem by introducing a new weak coupling regime that admits singularities compatible with both a crepant resolution and an orientifold symmetry. We also comment on possible applications of the new limit to model building. We finally discuss other unexpected phenomena as for example the existence of several non-equivalent directions to flow from strong to weak coupling leading to different gauge groups.Comment: 34 page

Wavefunctions and the Point of E8 in F-theory

In F-theory GUTs interactions between fields are typically localised at points of enhanced symmetry in the internal dimensions implying that the coefficient of the associated operator can be studied using a local wavefunctions overlap calculation. Some F-theory SU(5) GUT theories may exhibit a maximum symmetry enhancement at a point to E8, and in this case all the operators of the theory can be associated to the same point. We take initial steps towards the study of operators in such theories. We calculate wavefunctions and their overlaps around a general point of enhancement and establish constraints on the local form of the fluxes. We then apply the general results to a simple model at a point of E8 enhancement and calculate some example operators such as Yukawa couplings and dimension-five couplings that can lead to proton decay.Comment: 46 page

Froggatt-Nielsen models from E8 in F-theory GUTs

This paper studies F-theory SU(5) GUT models where the three generations of the standard model come from three different curves. All the matter is taken to come from curves intersecting at a point of enhanced E8 gauge symmetry. Giving a vev to some of the GUT singlets naturally implements a Froggatt-Nielsen approach to flavour structure. A scan is performed over all possible models and the results are filtered using phenomenological constraints. We find a unique model that fits observations of quark and lepton masses and mixing well. This model suffers from two drawbacks: R-parity must be imposed by hand and there is a doublet-triplet splitting problem.Comment: 42 pages; v2:journal version; v3:corrected typo in neutrino masse

Matter wave functions and Yukawa couplings in F-theory Grand Unification

We study the local structure of zero mode wave functions of chiral matter fields in F-theory unification. We solve the differential equations for the zero modes derived from local Higgsing in the 8-dimensional parent action of F-theory 7-branes. The solutions are found as expansions both in powers and derivatives of the magnetic fluxes. Yukawa couplings are given by an overlap integral of the three wave functions involved in the interaction and can be calculated analytically. We provide explicit expressions for these Yukawas to second order both in the flux and derivative expansions and discuss the effect of higher order terms. We explicitly describe the dependence of the couplings on the U(1) charges of the relevant fields, appropriately taking into account their normalization. A hierarchical Yukawa structure is naturally obtained. The application of our results to the understanding of the observed hierarchies of quarks and leptons is discussed.Comment: Latex, 51 pages, 4 figures, typos corrected, note adde

Massive Abelian Gauge Symmetries and Fluxes in F-theory

F-theory compactified on a Calabi-Yau fourfold naturally describes non-Abelian gauge symmetries through the singularity structure of the elliptic fibration. In contrast Abelian symmetries are more difficult to study because of their inherently global nature. We argue that in general F-theory compactifications there are massive Abelian symmetries, such as the uplift of the Abelian part of the U(N) gauge group on D7-branes, that arise from non-Kahler resolutions of the dual M-theory setup. The four-dimensional F-theory vacuum with vanishing expectation values for the gauge fields corresponds to the Calabi-Yau limit. We propose that fluxes that are turned on along these U(1)s are uplifted to non-harmonic four-form fluxes. We derive the effective four-dimensional gauged supergravity resulting from F-theory compactifications in the presence of the Abelian gauge factors including the effects of possible fluxes on the gauging, tadpoles and matter spectrum.Comment: 49 page

Flux and Instanton Effects in Local F-theory Models and Hierarchical Fermion Masses

We study the deformation induced by fluxes and instanton effects on Yukawa couplings involving 7-brane intersections in local F-theory constructions. In the absence of non-perturbative effects, holomorphic Yukawa couplings do not depend on open string fluxes. On the other hand instanton effects (or gaugino condensation on distant 7-branes) do induce corrections to the Yukawas. The leading order effect may also be captured by the presence of closed string (1,2) IASD fluxes, which give rise to a non-commutative structure. We check that even in the presence of these non-perturbative effects the holomorphic Yukawas remain independent of magnetic fluxes. Although fermion mass hierarchies may be obtained from these non-perturbative effects, they would give identical Yukawa couplings for D-quark and Lepton masses in SU(5) F-theory GUT's, in contradiction with experiment. We point out that this problem may be solved by appropriately normalizing the wavefunctions. We show in a simple toy model how the presence of hypercharge flux may then be responsible for the difference between D-quarks and Lepton masses in local SU(5) GUT's.Comment: 84 pages, 1 figure. v2: minor corrections and references adde

The Footprint of F-theory at the LHC

Recent work has shown that compactifications of F-theory provide a potentially attractive phenomenological scenario. The low energy characteristics of F-theory GUTs consist of a deformation away from a minimal gauge mediation scenario with a high messenger scale. The soft scalar masses of the theory are all shifted by a stringy effect which survives to low energies. This effect can range from 0 GeV up to ~ 500 GeV. In this paper we study potential collider signatures of F-theory GUTs, focussing in particular on ways to distinguish this class of models from other theories with an MSSM spectrum. To accomplish this, we have adapted the general footprint method developed recently for distinguishing broad classes of string vacua to the specific case of F-theory GUTs. We show that with only 5 fb^(-1) of simulated LHC data, it is possible to distinguish many mSUGRA models and low messenger scale gauge mediation models from F-theory GUTs. Moreover, we find that at 5 fb^(-1), the stringy deformation away from minimal gauge mediation produces observable consequences which can also be detected to a level of order ~ +/- 80 GeV. In this way, it is possible to distinguish between models with a large and small stringy deformation. At 50 fb^(-1), this improves to ~ +/- 10 GeV.Comment: 85 pages, 37 figure