1,228 research outputs found
The Origin of Families and Grand Unification
We exploit a recent advance in the study of topological superconductors to
propose a solution to the family puzzle of particle physics in the context of
SO(18) (or more correctly, Spin(18)) grand unification. We argue that Yukawa
couplings of intermediate strength may allow the mirror matter and extra
families to decouple at arbitrarily high energies. As was clear from the
existing literature, we have to go beyond the Higgs mechanism in order to solve
the family puzzle. A pattern of symmetry breaking which results in the SU(5)
grand unified theory with horizontal or family symmetry USp(4) = Spin(5) (or
more loosely, SO(5)) leaves exactly three light families of matter and seems
particularly appealing. We comment briefly on an alternative scheme involving
discrete non-abelian family symmetries. In a few lengthy appendices we review
some of the pertinent condensed matter theory.Comment: 31 pages, no figures. v2: minor changes, added subsection II.
See-Saw Masses for Quarks and Leptons in SU(5)
We build on a recent paper by Grinstein, Redi and Villadoro, where a see-saw
like mechanism for quark masses was derived in the context of spontaneously
broken gauged flavour symmetries. The see-saw mechanism is induced by heavy
Dirac fermions which are added to the Standard Model spectrum in order to
render the flavour symmetries anomaly-free. In this letter we report on the
embedding of these fermions into multiplets of an SU(5) grand unified theory
and discuss a number of interesting consequences.Comment: 15 pages, 4 figures (v3: outline restructured, modified mechanism to
cancel anomalies
F-theory and Neutrinos: Kaluza-Klein Dilution of Flavor Hierarchy
We study minimal implementations of Majorana and Dirac neutrino scenarios in
F-theory GUT models. In both cases the mass scale of the neutrinos m_nu ~
(M_weak)^2/M_UV arises from integrating out Kaluza-Klein modes, where M_UV is
close to the GUT scale. The participation of non-holomorphic Kaluza-Klein mode
wave functions dilutes the mass hierarchy in comparison to the quark and
charged lepton sectors, in agreement with experimentally measured mass
splittings. The neutrinos are predicted to exhibit a "normal" mass hierarchy,
with masses m_3,m_2,m_1 ~ .05*(1,(alpha_GUT)^(1/2),alpha_GUT) eV. When the
interactions of the neutrino and charged lepton sectors geometrically unify,
the neutrino mixing matrix exhibits a mild hierarchical structure such that the
mixing angles theta_23 and theta_12 are large and comparable, while theta_13 is
expected to be smaller and close to the Cabibbo angle: theta_13 ~ theta_C ~
(alpha_GUT)^(1/2) ~ 0.2. This suggests that theta_13 should be near the current
experimental upper bound.Comment: v2: 83 pages, 10 figures, references adde
Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
Theories defined in higher than four dimensions have been used in various
frameworks and have a long and interesting history. Here we review certain
attempts, developed over the last years, towards the construction of unified
particle physics models in the context of higher-dimensional gauge theories
with non-commutative extra dimensions. These ideas have been developed in two
complementary ways, namely (i) starting with a higher-dimensional gauge theory
and dimensionally reducing it to four dimensions over fuzzy internal spaces and
(ii) starting with a four-dimensional, renormalizable gauge theory and
dynamically generating fuzzy extra dimensions. We describe the above approaches
and moreover we discuss the inclusion of fermions and the construction of
realistic chiral theories in this context
Algebraic structures, physics and geometry from a Unified Field Theoretical framework
Starting from a Unified Field Theory (UFT) proposed previously by the author,
the possible fermionic representations arising from the same spacetime are
considered from the algebraic and geometrical viewpoint. We specifically
demonstrate in this UFT general context that the underlying basis of the single
geometrical structure P (G,M) (the principal fiber bundle over the real
spacetime manifold M with structural group G) reflecting the symmetries of the
different fields carry naturally a biquaternionic structure instead of a
complex one. This fact allows us to analyze algebraically and to interpret
physically in a straighforward way the Majorana and Dirac representations and
the relation of such structures with the spacetime signature and non-hermitian
(CP) dynamic operators. Also, from the underlying structure of the tangent
space, the existence of hidden (super) symmetries and the possibility of
supersymmetric extensions of these UFT models are given showing that
Rothstein's theorem is incomplete for that description. The importance of the
Clifford algebras in the description of all symmetries, mainly the interaction
of gravity with the other fields, is briefly discussed.Comment: To be published in IJTP, last corrected version. This work is devoted
to the memory of the Prof. Academician Vladimir Georgievich Kadyshevsky. 21
pages, no figures. References added and misprints/typos correcte
An infinite supermultiplet of massive higher-spin fields
The representation theory underlying the infinite-component relativistic wave
equation written by Majorana is revisited from a modern perspective. On the one
hand, the massless solutions of this equation are shown to form a
supermultiplet of the superPoincare algebra with tensorial central charges; it
can also be obtained as the infinite spin limit of massive solutions. On the
other hand, the Majorana equation is generalized for any space-time dimension
and for arbitrary Regge trajectories. Inspired from these results, an infinite
supermultiplet of massive fields of all spins and of equal mass is constructed
in four dimensions and proved to carry an irreducible representation of the
orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial
charges.Comment: 29 pages, references [30] added. To appear in JHE
Unification of Force and Substance
Maxwell's mature presentation of his equations emphasized the unity of
electromagnetism and mechanics, subsuming both as "dynamical systems". That
intuition of unity has proved both fruitful, as a source of pregnant concepts,
and broadly inspiring. A deep aspect of Maxwell's work is its use of redundant
potentials, and the associated requirement of gauge symmetry. Those concepts
have become central to our present understanding of fundamental physics, but
they can appear to be rather formal and esoteric. Here I discuss two things:
The physical significance of gauge invariance, in broad terms; and some
tantalizing prospects for further unification, building on that concept, that
are visible on the horizon today. If those prospects are realized, Maxwell's
vision of the unity of field and substance will be brought to a new level.Comment: Talk at Royal Society Symposium, "Unifying Physics and Technology in
the Light of Maxwell's Equations", November 2015. 26 pages, no figure
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