A D-brane inspired U(3)_CxU(3)_LxU(3)_R model

Motivated by D-brane scenarios, we consider a non-supersymmetric model based on the gauge symmetry U(3)_CxU(3)_LxU(3)_R$ which is equivalent to the SU(3)^3 ``trinification'' model supplemented by three U(1)s. Two U(1) combinations are anomalous while the third U(1)_Z' is anomaly free and contributes to the hypercharge generator. This hypercharge embedding correspods to sin^2\theta_W=6/19 in the case of full gauge coupling unification. The U(3)^3 symmetry is broken down to the Standard Model by vev's of two (1,3,\bar3)- scalar multiplets supplemented by two Higgs fields in (1,3,1) and (1,1,3) representations. The latter break U(1)_Z' and provide heavy masses to the extra lepton doublets. Fermions belong to (3,\bar 3,1)+(\bar 3,1,3)+ (1,3,\bar 3) representations as in the trinification model. The model predicts a natural quark-lepton hierarchy, since quark masses are obtained from tree-level couplings, while charged leptons receive masses from fourth order Yukawa terms, as a consequence of the extra abelian symmetries. Light Majorana neutrino masses are obtained through a see-saw type mechanism operative at the SU(3)_R breaking scale of the order M_R\ge 10^9 GeV.Comment: 10 pages, 2 figure

Discrete Flavour Symmetries from the Heisenberg Group

Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular in the $PSL_2(p)$ groups which contain the phenomenologically interesting cases.Comment: 16 page

Uncertainty relation and non-dispersive states in Finite Quantum Mechanics

In this letter, we provide evidence for a classical sector of states in the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position -momentum uncertainty (equivalent to an effective $\hbar$) vanishes. The classical regime, contrary to standard Quantum Mechanical Systems of particles and fields, but also of strings and branes appears in short distances of the order of the lattice spacing. {}For linear quantum maps of long periods, we observe that time evolution leads to fast decorrelation of the wave packets, phenomenon similar to the behavior of wave packets in t' Hooft and Susskind holographic picture. Moreoever, we construct explicitly a non - dispersive basis of states in accordance with t' Hooft's arguments about the deterministic behavior of FQM.Comment: Latex file, 16pages, 3 ps-figures, version to appear in Phys.Lett.

A Pati-Salam model from branes

We explore the possibility of embedding the Pati-Salam model in the context of Type I brane models. We study a generic model with U(4)_C x U(2)_L x U(2)_R gauge symmetry and matter fields compatible with a Type I brane configuration. Examining the anomaly cancellation conditions of the surplus abelian symmetries we find an alternative hypercharge embedding that is compatible with a low string/brane scale of the order of 5-7 TeV, when the U(4)_C and U(2)_R brane stack couplings are equal. Proton stability is assured as baryon number is associated to a global symmetry remnant of the broken abelian factors. It is also shown that this scenario can accommodate an extra low energy abelian symmetry that can be associated to lepton number. The issue of fermion and especially neutrino masses is also discussed.Comment: 14 pages, 1 figure, final version to be published in Phys. Lett.

F-GUTs with Mordell-Weil U(1)'s

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 are induced on the coefficients of its Tate form. Converting the equation representing the generic hypersurface $P_{112}$ to this Tate's 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 ${\cal E}_6\times U(1)$ effective F-theory model.Comment: 13 page