2,921 research outputs found
Possible Origin of Fermion Chirality and Gut Structure From Extra Dimensions
The fundamental chiral nature of the observed quarks and leptons and the
emergence of the gauge group itself are most puzzling aspects of the standard
model. Starting from general considerations of topological properties of gauge
field configurations in higher space-time dimensions, it is shown that the
existence of non-trivial structures in ten dimensions would determine a class
of models corresponding to a grand unified GUT structure with complex fermion
representations with respect to . The
discussion is carried out within the framework of string theories with
characteristic energy scales below the Planck mass. Avoidance of topological
obstructions upon continuous deformation of field configurations leads to
global chiral symmetry breaking of the underlying fundamental theory, imposes
rigorous restrictions on the structure of the vacuum and space-time itself and
determines uniquely the gauge structure and matter content.Comment: final version to appear in Phys. Rev.
The Status of the Minimal Supersymmetric Standard Model and Beyond
The minimal supersymmetric extension of the Standard Model (MSSM) is
reviewed. In the most general framework with minimal field content and R-parity
conservation, the MSSM is a 124-parameter model (henceforth called MSSM-124).
An acceptable phenomenology occurs only at exceptional points (and small
perturbations around these points) of MSSM-124 parameter space. Among the
topics addressed in this review are: gauge coupling unification, precision
electroweak data, phenomenology of the MSSM Higgs sector, and supersymmetry
searches at present and future colliders. The implications of approaches beyond
the MSSM are briefly addressed.Comment: 17 pages, LaTeX, with espcrc2.sty style file, to appear in the
Proceedings of the 5th International Conference on Supersymmetries in Physics
(SUSY 97
Small symplectic Calabi-Yau surfaces and exotic 4-manifolds via genus-3 pencils
We explicitly produce symplectic genus-3 Lefschetz pencils (with base
points), whose total spaces are homeomorphic but not diffeomorphic to rational
surfaces CP^2 # p (-CP^2) for p= 7, 8, 9. We then give a new construction of an
infinite family of symplectic Calabi-Yau surfaces with first Betti number
b_1=2,3, along with a surface with b_1=4 homeomorphic to the 4-torus. These are
presented as the total spaces of symplectic genus-3 Lefschetz pencils we
construct via new positive factorizations in the mapping class group of a
genus-3 surface. Our techniques in addition allow us to answer in the negative
a question of Korkmaz regarding the upper bound on b_1 of a genus-g fibration.Comment: 29 pages, 6 figures. Corrected several typo
Uniform Cyclic Group Factorizations of Finite Groups
In this paper, we introduce a kind of decomposition of a finite group called
a uniform group factorization, as a generalization of exact factorizations of a
finite group. A group is said to admit a uniform group factorization if
there exist subgroups such that and the number of ways to represent any element as () does not depend on the choice of . Moreover, a
uniform group factorization consisting of cyclic subgroups is called a uniform
cyclic group factorization. First, we show that any finite solvable group
admits a uniform cyclic group factorization. Second, we show that whether all
finite groups admit uniform cyclic group factorizations or not is equivalent to
whether all finite simple groups admit uniform group factorizations or not.
Lastly, we give some concrete examples of such factorizations.Comment: 10 pages. To appear in Communications in Algebr
Computing images of Galois representations attached to elliptic curves
Let E be an elliptic curve without complex multiplication (CM) over a number
field K, and let G_E(ell) be the image of the Galois representation induced by
the action of the absolute Galois group of K on the ell-torsion subgroup of E.
We present two probabilistic algorithms to simultaneously determine G_E(ell) up
to local conjugacy for all primes ell by sampling images of Frobenius elements;
one is of Las Vegas type and the other is a Monte Carlo algorithm. They
determine G_E(ell) up to one of at most two isomorphic conjugacy classes of
subgroups of GL_2(Z/ell Z) that have the same semisimplification, each of which
occurs for an elliptic curve isogenous to E. Under the GRH, their running times
are polynomial in the bit-size n of an integral Weierstrass equation for E, and
for our Monte Carlo algorithm, quasi-linear in n. We have applied our
algorithms to the non-CM elliptic curves in Cremona's tables and the
Stein--Watkins database, some 140 million curves of conductor up to 10^10,
thereby obtaining a conjecturally complete list of 63 exceptional Galois images
G_E(ell) that arise for E/Q without CM. Under this conjecture we determine a
complete list of 160 exceptional Galois images G_E(ell) the arise for non-CM
elliptic curves over quadratic fields with rational j-invariants. We also give
examples of exceptional Galois images that arise for non-CM elliptic curves
over quadratic fields only when the j-invariant is irrational.Comment: minor edits, 47 pages, to appear in Forum of Mathematics, Sigm
Emergent symmetries in the canonical tensor model
The canonical tensor model (CTM) is a tensor model proposing a classically
and quantum mechanically consistent model of gravity, formulated as a
first-class constraint system with structural similarities to the ADM formalism
of general relativity. A recent study on the formal continuum limit of the
classical CTM has shown that it produces a general relativistic system. This
formal continuum limit assumes the emergence of a continuous space, but
ultimately continuous spaces should be obtained as preferred configurations of
the quantum CTM. In this paper we study the symmetry properties of a wave
function which exactly solves the quantum constraints of the CTM for general
. We have found that it has strong peaks at configurations invariant under
some Lie-groups, as predicted by a mechanism described in our previous paper. A
surprising result was the preference of configurations invariant not only under
Lie-groups with positive signatures, but also with spacetime-like signatures,
i.e., . Such symmetries could characterize the global structures of
spacetimes, and our results are encouraging towards showing spacetime emergence
in the CTM. To verify the asymptotic convergence of the wave function we have
also analyzed the asymptotic behaviour, which for the most part seems to be
well under control.Comment: 40 pages, 9 figures; Typos corrected. Minor changes. A reference
adde
Low-Energy Supersymmetry and its Phenomenology
The structure of low-energy supersymmetric models of fundamental particles
and interactions is reviewed, with an emphasis on the minimal supersymmetric
extension of the Standard Model (MSSM) and some of its variants. Various
approaches to the supersymmetry-breaking mechanism are considered. The
implications for the phenomenology of Higgs bosons and supersymmetric particles
at future colliders are discussed.Comment: 20 pages, 2 figures, LaTeX with espcrc2.sty, invited talk at the "30
Years of Supersymmetry" Symposium, Minneapolis, Minnesota, 13--15 October
200
Precision Unification and Proton Decay in F-Theory GUTs with High Scale Supersymmetry
F-theory GUTs provide a promising UV completion for models with approximate
gauge coupling unification, such as the (non-supersymmetric) Standard Model.
More specifically, if the superparters have masses well above the TeV scale,
the resulting imperfection in unification can be accounted for by the, in
principle calculable, classical F-theory correction at the high scale. In this
paper we argue for the correct form of the F-theory corrections to unification,
including KK mode loop effects. However, the price of compensating the
imprecise unification in such High Scale SUSY models with F-theory corrections
is that the GUT scale is lowered, potentially leading to a dangerously high
proton decay rate from dimension-6 operators. We analyse the possibility of
suppressing the decay rate by the localization of gauge bosons in higher
dimensions. While this effect can be very strong for the zero modes, we find
that in the simplest models of this type it is difficult to realize a
significant suppression for higher modes (Landau levels). Notably, in the
absence of substantial suppressions to the proton decay rate, the superpartners
must be lighter than 100 TeV to satisfy proton decay constraints. We highlight
that multiple correlated signals of proton decay could verify this scenario.Comment: 44 pages. v2: References adde
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