F-theory GUTs Research Articles

On the GUT scale of F-theory [formula omitted

In F-theory GUTs, threshold corrections from Kaluza–Klein (KK) massive modes arising from gauge and matter multiplets play an important role in the determination of the weak mixing angle and the strong gauge coupling of the effective low energy model. In this Letter we further explore the induced modifications on the gauge couplings running and the GUT scale. In particular, we focus on the KK-contributions from matter curves and analyze the conditions on the chiral and Higgs matter spectrum which imply a GUT scale consistent with the minimal unification scenario. As an application, we present an explicit computation of these thresholds for matter fields residing on specific non-trivial Riemann surfaces.

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.

The conformal sector of F-theory GUTs

D3-brane probes of exceptional Yukawa points in F-theory GUTs are natural hidden sectors for particle phenomenology. We find that coupling the probe to the MSSM yields a new class of N = 1 conformal fixed points with computable infrared R-charges. Quite surprisingly, we find that the MSSM only weakly mixes with the strongly coupled sector in the sense that the MSSM fields pick up small exactly computable anomalous dimensions. Additionally, we find that although the states of the probe sector transform as complete GUT multiplets, their coupling to Standard Model fields leads to a calculable threshold correction to the running of the visible sector gauge couplings which improves precision unification. We also briefly consider scenarios in which SUSY is broken in the hidden sector. This leads to a gauge mediated spectrum for the gauginos and first two superpartner generations, with additional contributions to the third generation superpartners and Higgs sector.

T-branes and monodromy

We introduce T-branes, or "triangular branes," which are novel non-abelian bound states of branes characterized by the condition that on some loci, their matrix of normal deformations, or Higgs field, is upper triangular. These configurations refine the notion of monodromic branes which have recently played a key role in F-theory phenomenology. We show how localized matter living on complex codimension one subspaces emerge, and explain how to compute their Yukawa couplings, which are localized in complex codimension two. Not only do T-branes clarify what is meant by brane monodromy, they also open up a vast array of new possibilities both for phenomenological constructions and for purely theoretical applications. We show that for a general T-brane, the eigenvalues of the Higgs field can fail to capture the spectrum of localized modes. In particular, this provides a method for evading some constraints on F-theory GUTs which have assumed that the spectral equation for the Higgs field completely determines a local model.

Baryon and dark matter genesis from strongly coupled strings

D3-brane probes of E-type Yukawa points lead to strongly coupled nearly conformal sectors nearby the Standard Model (visible sector) which are motivated by F-theory GUTs. Realistic visible sector brane configurations induce a seesaw mass hierarchy in the hidden sector with light GUT singlets charged under a strongly coupled hidden sector U(1). Interpreting these GUT singlets as dark matter, this leads to a matter genesis scenario where the freeze out and subsequent decay of heavy mediators between the two sectors simultaneously populates comparable amounts of baryon and dark matter asymmetry. Generating a net matter asymmetry requires a generational structure in the probe sector which is absent at weak string coupling, but is automatically realized at strong string coupling via towers of dyonic bound states corresponding to multi-prong string junctions. The hidden U(1) couples to the visible sector through both electric and magnetic kinetic mixing terms, providing an efficient means to deplete the symmetric component of dark matter. The mass of the dark matter is of order ~ 10 GeV. The dark matter mass and the matter asymmetry are both controlled by the scale of conformal symmetry breaking ~ 10^(9) - 10^(13) GeV, with the precise relation between the two set by details of the visible sector brane configuration.

CPviolation in hierarchical Yukawa models

Because 4-dimensional CP is a good symmetry of many higher-dimensional theories, this suggests the possible existence of a universal CP-violating phase originating from the process of compactification. Such a phase, if it existed, would not be easy to uncover since the phases in Yukawa matrices are not simply related to the observed CKM phase $\delta$. Hierarchical Yukawa models of the type arising in F-theory GUT models provide an interesting exception. Recently, Heckman and Vafa studied a particular F-theory GUT model with hierarchical Yukawa matrices with complex phases of O(1) and showed, by examining the Jarlskog invariant, that this model leads to $\sin \delta \sim O(1)$. A more detailed examination of the model, although confirming their result, is seen to be also compatible with having a phase $\delta_o= \pi/3$ imprinted on the Hermitian Yukawa matrices, leading to $\sin \delta \simeq \sin \delta_o$.

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.

Hypercharge Flux, Exotics, and Anomaly Cancellation inF-theory Grand Unification

We sharpen constraints related to hypercharge flux in F-theory grand unified theories that possess U(1) symmetries and argue that they arise as a consequence of four-dimensional anomaly cancellation. This gives a physical explanation for all restrictions that were observed in spectral cover models while demonstrating that the phenomenological implications for a well-motivated set of models are not tied to any particular formalism.

Yukawa couplings and fermion mass structure in F-theory GUTs

The calculation of Yukawa couplings in F-theory GUTs is developed. The method is applied to the top and bottom Yukawa couplings in an SU(5) model of fermion masses based on family symmetries coming from the SU(5)_\perp factor in the underlying E(8) theory. The remaining Yukawa couplings involving the light quark generations are determined by the Froggatt Nielsen non-renormalisable terms generated by heavy messenger states. We extend the calculation of Yukawa couplings to include massive states and estimate the full up and down quark mass matrices in the SU(5) model. We discuss the new features of the resulting structure compared to what is usually assumed for Abelian family symmetry models and show how the model can give a realistic quark mass matrix structure. We extend the analysis to the neutrino sector masses and mixing where we find that tri-bi-maximal mixing is readily accommodated. Finally we discuss mechanisms for splitting the degeneracy between the charged leptons and the down quarks and the doublet triplet splitting in the Higgs sector.

An exceptional sector for F-theory GUTs

D3-branes are often a necessary ingredient in global compactifications of F-theory. In minimal realizations of flavor hierarchies in F-theory GUT models, suitable fluxes are turned on, which in turn attract D3-branes to the Yukawa points. Of particular importance are ``E-type'' Yukawa points, as they are required to realize a large top quark mass. In this paper we study the worldvolume theory of a D3-brane probing such an E-point. D3-brane probes of isolated exceptional singularities lead to strongly coupled $\mathcal{N}=2$ conformal field theories (CFTs) of the type found by Minahan and Nemeschansky. We show that the local data of an E-point probe theory determine an $\mathcal{N}=1$ deformation of the original $\mathcal{N}=2$ theory which couples this strongly interacting CFT to a free hypermultiplet. Monodromy in the seven-brane configuration translates to a novel class of deformations of the CFT. We study how the probe theory couples to the standard model, determining the most relevant F-term couplings, the effect of the probe on the running of the standard model gauge couplings, as well as possible sources of kinetic mixing with the standard mModel.

Toric Methods in F-Theory Model Building

We discuss recent constructions of global F-theory GUT models and explain how to make use of toric geometry to do calculations within this framework. After introducing the basic properties of global F-theory GUTs, we give a self-contained review of toric geometry and introduce all the tools that are necessary to construct and analyze global F-theory models. We will explain how to systematically obtain a large class of compact Calabi-Yau fourfolds which can support F-theory GUTs by using the software package PALP.

Global F-theory models: instantons and gauge dynamics

We elucidate certain aspects of F-theory gauge dynamics, due to quantum splitting of certain brane stacks, which are absent in the Type IIB limit. We also provide a working implementation of an algorithm for computing cohomology of line bundles on arbitrary toric varieties. This should be of general use for studying the physics of global Type IIB and F-theory models, in particular for the explicit counting of zero modes for rigid F-theory instantons which contribute to charged matter couplings. We illustrate the discussion by constructing and analyzing in detail a compact F-theory GUT model in which a D-brane instanton generates the top Yukawa coupling non-perturbatively.

A note on G-fluxes for F-theory model building

We propose a description of G-fluxes that induce chirality in 4-dimensional F-theory GUT spectra that is intrinsic to F-theory and does not rely on Heterotic/F-theory duality. Using this, we describe how to globally extend fluxes that have been constructed in a semi-local setting and obtain an F-theoretic formula for computing the chiral spectrum that they induce. Chirality computations agree with those from the semi-local Higgs bundle analysis for matter fields that are charged under the GUT-group, and hence with the standard Heterotic formulae where applicable. Finally, the relation of G-fluxes to SU(5)_{perp} bundles on the F-theory 4-fold is discussed and used to motivate a quantization rule that is consistent both with the Higgs bundle one as well as the Heterotic one when a Heterotic dual exists.

$ \mathcal{N} = 1 $ SCFTs from brane monodromy

We present evidence for a new class of strongly coupled N = 1 superconformal field theories (SCFTs) motivated by F-theory GUT constructions. These SCFTs arise from D3-brane probes of tilted seven-branes which undergo monodromy. In the probe theory, this tilting corresponds to an N = 1 deformation of an N = 2 SCFT by a matrix of field-dependent masses with non-trivial branch cuts in the eigenvalues. Though these eigenvalues characterize the geometry, we find that they do not uniquely specify the holomorphic data of the physical theory. We also comment on some phenomenological aspects of how these theories can couple to the visible sector. Our construction can be applied to many N = 2 SCFTs, resulting in a large new class of N = 1 SCFTs.

CP violation and F-theory GUTs

Recent work on F-theory GUTs has shown that the predicted masses and magnitudes of the mixing matrix elements in the quark and lepton sectors are in close accord with experiment. In this Letter we estimate the CP violating phase of the mixing matrices by considering the Jarlskog invariant. We find by carefully treating certain cancellations in the computation of the Jarlskog invariant that |Jquark|∼αGUT3∼6×10−5, and that the CP violating phase of the quark sector is large, in accord with experiment. Moreover, we predict (up to order one factors) that |Jlepton|∼αGUT∼4×10−2 and that the CP violating phase of the lepton sector is also large.

Abelian gauge symmetries and proton decay in globalF-theory GUTs

The existence of abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau fourfold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such U(1) symmetries along the Coulomb and the Higgs branch. As one application we examine abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In SU(5) GUT models this mechanism enforces a global U(1)_X symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau fourfolds and their mirror duals starting from an underlying E_8 and E_7 x U(1) enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyse F-theory GUT models.

Global SO(10) F-theory GUTs

Making use of toric geometry we construct a class of global F-theory GUT models. The base manifolds are blowups of Fano threefolds and the Calabi-Yau fourfold is a complete intersection of two hypersurfaces. We identify possible GUT divisors and construct SO(10) models on them using the spectral cover construction. We use a split spectral cover to generate chiral matter on the 10 curves in order to get more degrees of freedom in phenomenology. We use abelian flux to break SO(10) to SU(5) ×U(1) which is interpreted as a flipped SU(5) model. With the GUT Higgses in the SU(5) × U(1) model it is possible to further break the gauge symmetry to the Standard Model. We present several phenomenologically attractive examples in detail.

F-theory and the LHC: stau search

F-theory GUT models favor a relatively narrow range of soft supersymmetry breaking parameters in the MSSM Lagrangian. This leads to the specific predictions that a 10 − 100 MeV mass gravitino is the LSP, and the NLSP is quasi-stable, with a lifetime between a second to an hour. In a wide range of parameter space, the NLSP turns out to be a stau, though a bino-like lightest neutralino is also possible. Focusing on F-theory GUTs with a stau NLSP, we study the discovery potential at the LHC for such scenarios. Models with a quasi-stable stau predict a striking signature of a heavy charged particle passing through the detector. As a function of the parameters of minimal F-theory GUTs, we study how many of such events to expect, and additional signatures correlated with the presence of quasi-stable staus. We also study the prospects for staus to become stopped in or near the detector, as well as potential ways to distinguish such models from minimal gauge mediation models with similar spectra.

On hypercharge flux and exotics in F-theory GUTs

We study SU(5) Grand Unified Theories within a local framework in F-theory with multiple extra U(1) symmetries arising from a small monodromy group. The use of hypercharge flux for doublet-triplet splitting implies massless exotics in the spectrum that are protected from obtaining a mass by the U(1) symmetries. We find that lifting the exotics by giving vacuum expectation values to some GUT singlets spontaneously breaks all the U(1) symmetries which implies that proton decay operators are induced. If we impose an additional R-parity symmetry by hand we find all the exotics can be lifted while proton decay operators are still forbidden. These models can retain the gauge coupling unification accuracy of the MSSM at 1-loop. For models where the generations are distributed across multiple curves we also present a motivation for the quark-lepton mass splittings at the GUT scale based on a Froggatt-Nielsen approach to flavour.

The point of E 8 in F-theory GUTs

We show that in F-theory GUTs, a natural explanation of flavor hierarchies in the quark and lepton sector requires a single point of E_8 enhancement in the internal geometry, from which all Yukawa couplings originate. The monodromy group acting on the seven-brane configuration plays a key role in this analysis. Moreover, the E_8 structure automatically leads to the existence of the additional fields and interactions needed for minimal gauge mediated supersymmetry breaking,__and almost nothing else__. Surprisingly, we find that in all but one Dirac neutrino scenario the messenger fields in the gauge mediated supersymmetry breaking sector transform as vector-like pairs in the 10 + 10* of SU(5). We also classify dark matter candidates available from this enhancement point, and rule out both annihilating and decaying dark matter scenarios as explanations for the recent experiments PAMELA, ATIC and FERMI. In F-theory GUT models, a 10-100 MeV mass gravitino remains as the prime candidate for dark matter, thus suggesting an astrophysical origin for recent experimental signals.