236 research outputs found
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 groups which contain the phenomenologically
interesting cases.Comment: 16 page
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
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 ) 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 '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 to this Tate's
form we find that the presence of a U(1), already in this local description, is
consistent with the exceptional and non-abelian
singularities. We briefly comment on a viable effective
F-theory model.Comment: 13 page
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