In this note we study the constraints on F-theory GUTs with extra $U(1)$s in the context of elliptic fibrations with rational sections. We consider the simplest case of one abelian factor (Mordell-Weil rank one) and investigate the conditions that ar
e induced on the coefficients of its Tate form. Converting the equation representing the generic hypersurface $P_{112}$ to this Tates form we find that the presence of a U(1), already in this local description, is consistent with the exceptional ${cal E}_6$ and ${cal E}_7$ non-abelian singularities. We briefly comment on a viable ${cal E}_6times U(1)$ effective F-theory model.
We investigate the possibility of expressing the charged leptons and neutrino mass matrices as linear combinations of generators of a single finite group. Constraints imposed on the resulting mixing matrix by current data restrict the group types, bu
t allow a non zero value for the theta_13 mixing angle
Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we exa
mine the consequences of the simple hypothesis that the three-dimensional space has a global R^2 X S^1 topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newtons gravitational potential and we find that for distances smaller than the S^1-radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newtons force from 1/r^2 to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level.
In F-theory GUTs, threshold corrections from Kaluza-Klein 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 analyse 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.
The fermion mass textures are discussed in the context of F-theory SU(5) GUT. The tree-level up, down and charged lepton Yukawa couplings are computed in terms of the integrals of overlapping wavefunctions at the intersection points of three matter c
urves. All remaining entries in the fermion mass matrices can also be reliably estimated from higher order non-renormalizable Yukawa couplings mediated by heavy string modes and/or Kaluza-Klein states.
In a class of F-theory SU(5) GUTs the low energy chiral mass spectrum is obtained from rank one fermion mass textures with a hierarchical structure organised by U(1) symmetries embedded in the exceptional E_8 group. In these theories chiral fields re
side on matter `curves and the tree level masses are computed from integrals of overlapping wavefuctions of the particles at the triple intersection points. This calculation requires knowledge of the exact form of the wavefuctions. In this work we propose a way to obtain a reliable estimate of the various quantities which determine the strength of the Yukawa couplings. We use previous analysis of KK threshold effects to determine the (ratios of) heavy mass scales of the theory which are involved in the normalization of the wave functions. We consider similar effects from the chiral spectrum of these models and discuss possible constraints on the emerging matter content. In this approach, we find that the Yukawa couplings can be determined solely from the U(1) charges of the states in the `intersection and the torsion which is a topological invariant quantity. We apply the results to a viable SU(5) model with minimal spectrum which satisfies all the constraints imposed by our analysis. We use renormalization group analysis to estimate the top and bottom masses and find that they are in agreement with the experimental values.
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) th
eory. 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.
We discuss F-theory SU(5) GUTs in which some or all of the quark and lepton families are assigned to different curves and family symmetry enforces a leading order rank one structure of the Yukawa matrices. We consider two possibilities for the suppre
ssion of baryon and lepton number violation. The first is based on Flipped SU(5) with gauge group SU(5)times U(1)_chi times SU(4)_{perp} in which U(1)_{chi} plays the role of a generalised matter parity. We present an example which, after imposing a Z_2 monodromy, has a U(1)_{perp}^2 family symmetry. Even in the absence of flux, spontaneous breaking of the family symmetry leads to viable quark, charged lepton and neutrino masses and mixing. The second possibility has an R-parity associated with the symmetry of the underlying compactification manifold and the flux. We construct an example of a model with viable masses and mixing angles based on the gauge group SU(5)times SU(5)_{perp} with a U(1)_{perp}^3 family symmetry after imposing a Z_2 monodromy.
