70 research outputs found
Minimal Standard Heterotic String Models
Three generation heterotic-string vacua in the free fermionic formulation
gave rise to models with solely the MSSM states in the observable Standard
Model charged sector. The relation of these models to Z_2 x Z_2 orbifold
compactifications dictates that they produce three pairs of untwisted Higgs
multiplets. The reduction to one pair relies on the analysis of supersymmetric
flat directions, that give superheavy mass to the dispensable Higgs states. We
explore the removal of the extra Higgs representations by using the free
fermion boundary conditions and hence directly at the string level, rather than
in the effective low energy field theory. We present a general mechanism that
achieves this reduction by using asymmetric boundary conditions between the
left- and right-moving internal fermions. We incorporate this mechanism in
explicit string models containing three twisted generations and a single
untwisted Higgs doublet pair. We further demonstrate that an additional effect
of the asymmetric boundary conditions is to substantially reduce the
supersymmetric moduli space.Comment: 20 pages, LaTeX; added reference
Z_2 x Z_2 Heterotic Orbifold Models of Non Factorisable Six Dimensional Toroidal Manifolds
We discuss heterotic strings on Z_2 x Z_2 orbifolds of non factorisable
six-tori. Although the number of fixed tori is reduced as compared to the
factorisable case, Wilson lines are still needed for the construction of three
generation models. An essential new feature is the straightforward appearance
of three generation models with one generation per twisted sector. We
illustrate our general arguments for the occurrence of that property by an
explicit example. Our findings give further support for the conjecture that
four dimensional heterotic strings formulated at the free fermionic point are
related to Z_2 x Z_2 orbifolds.Comment: 33 pages, LaTeX; discussion of modular invariance added in section
four; added references; to be published in JHE
OPERA data and The Equivalence Postulate of Quantum Mechanics
An interpretation of the recent results reported by the OPERA collaboration
is that neutrinos propagation in vacuum exceeds the speed of light. It has been
further been suggested that this interpretation can be attributed to the
variation of the particle speed arising from the Relativistic Quantum Hamilton
Jacobi Equation. I show that this is in general not the case. I derive an
expression for the quantum correction to the instantaneous relativistic
velocity in the framework of the relativistic quantum Hamilton-Jacobi equation,
which is derived from the equivalence postulate of quantum mechanics. While the
quantum correction does indicate deviations from the classical energy--momentum
relation, it does not necessarily lead to superluminal speeds. The quantum
correction found herein has a non-trivial dependence on the energy and mass of
the particle, as well as on distance travelled. I speculate on other possible
observational consequences of the equivalence postulate approach.Comment: 8 pages. Standard LaTex. References adde
Investigation of Quasi--Realistic Heterotic String Models with Reduced Higgs Spectrum
Quasi--realistic heterotic-string models in the free fermionic formulation
typically contain an anomalous U(1), which gives rise to a Fayet-Iliopolous
term that breaks supersymmetry at the one--loop level in string perturbation
theory. Supersymmetry is restored by imposing F- and D-flatness on the vacuum.
In Phys. Rev. D 78 (2008) 046009, we presented a three generation free
fermionic standard-like model which did not admit stringent F- and D-flat
directions, and argued that the all the moduli in the model are fixed. The
particular property of the model was the reduction of the untwisted Higgs
spectrum by a combination of symmetric and asymmetric boundary conditions with
respect to the internal fermions associated with the compactified dimensions.
In this paper we extend the analysis of free fermionic models with reduced
Higgs spectrum to the cases in which the SO(10) symmetry is left unbroken, or
is reduced to the flipped SU(5) subgroup. We show that all the models that we
study in this paper do admit stringent flat directions. The only examples of
models that do not admit stringent flat directions remain the strandard-like
models of reference Phys. Rev. D 78 (2008) 046009.Comment: 38 pages, 1 figur
On the Possibility of Optical Unification in Heterotic Strings
Recently J. Giedt discussed a mechanism, entitled optical unification,
whereby string scale unification is facilitated via exotic matter with
intermediate scale mass. This mechanism guarantees that a virtual MSSM
unification below the string scale is extrapolated from the running of gauge
couplings upward from M_Z^o when an intermediate scale desert is assumed. In
this letter we explore the possibility of optical unification within the
context of weakly coupled heterotic strings. In particular, we investigate this
for models of free fermionic construction containing the NAHE set of basis
vectors. This class is of particular interest for optical unification, because
it provides a standard hypercharge embedding within SO(10), giving the standard
k_Y = 5/3 hypercharge level, which was shown necessary for optical unification.
We present a NAHE model for which the set of exotic SU(3)_C
triplet/anti-triplet pairs, SU(2)_L doublets, and non-Abelian singlets with
hypercharge offers the possibility of optical unification. Whether this model
can realize optical unification is conditional upon these exotics not receiving
Fayet-Iliopoulos (FI) scale masses when a flat direction of scalar vacuum
expectation values is non-perturbatively chosen to cancel the FI D-term, xi,
generated by the anomalous U(1)-breaking Green-Schwarz-Dine-Seiberg-Wittten
mechanism. A study of perturbative flat directions and their phenomenological
implications for this model is underway.
This paper is a product of the NFS Research Experiences for Undergraduates
and the NSF High School Summer Science Research programs at Baylor University.Comment: 16 pages. Standard Late
String derived MSSM and M-theory Unification
The recent conjecture of possible equivalence between the string scale
and the minimal supersymmetric standard model unification scale M_U ~ 2.5 x
10^{16} GeV is considered in the context of string models. This conjecture
suggests that the observable gauge group just below the string scale should be
SU(3)_C x SU(2)_L x U(1)_Y and that the SU(3)_C x SU(2)_L x U(1)_Y-charged
spectrum of the observable sector should consist solely of the MSSM spectrum.
We demonstrate that string models can actually be constructed that possess
these observable features. Two aspects generic to many classes of three family
SU(3)_C x SU(2)_L x U(1)_Y string models are both an extra local anomalous
U(1)_A and numerous (often fractionally charged) exotic particles beyond the
MSSM. Thus, for these classes, the key to obtaining an M_S = M_U ~ 2.5 x
10^{16} GeV string model is the existence of F- and D-flat directions that near
the string scale can simultaneously break the anomalous U(1) and give mass to
all exotic SM-charged observable particles, decoupling them from the low energy
spectrum. In this letter we show, in the context of free fermionic strings,
that string models with flat directions possessing these features do exist. We
present one such string derived model in which all such exotic observable
states beyond the MSSM receive mass at the scale generated by the Fayet-
Iliopoulos term. The associated F- and D-flat direction is proven flat to all
orders of the superpotential.Comment: 18 pages. Standard Latex. Version to appear in PL
A Minimal Superstring Standard Model II: A Phenomenological Study
Recently, we demonstrated the existence of heterotic--string solutions in
which the observable sector effective field theory just below the string scale
reduces to that of the MSSM, with the standard observable gauge group being
just SU(3)_C x SU(2)_L x U(1)_Y and the SU(3)_C x SU(2)_L x U(1)_Y-charged
spectrum of the observable sector consisting solely of the MSSM spectrum.
Associated with this model is a set of distinct flat directions of vacuum
expectation values (VEVs) of non-Abelian singlet fields that all produce solely
the MSSM spectrum. In this paper, we study the effective superpotential induced
by these choices of flat directions. We investigate whether sufficient degrees
of freedom exist in these singlet flat directions to satisfy various
phenomenological constraints imposed by the observed Standard Model data. For
each flat direction, the effective superpotential is given to sixth order. The
variations in the singlet and hidden sector low energy spectrums are analyzed.
We then determine the mass matrices (to all finite orders) for the three
generations of MSSM quarks and leptons. Possible Higgs mu-terms are
investigated. We conclude by considering generalizations of our flat directions
involving VEVs of non-Abelian fields.Comment: 41 pages. Standard Late
Toward the M(F)--Theory Embedding of Realistic Free-Fermion Models
We construct a Landau-Ginzburg model with the same data and symmetries as a
orbifold that corresponds to a class of realistic free-fermion
models. Within the class of interest, we show that this orbifolding connects
between different orbifold models and commutes with the mirror
symmetry. Our work suggests that duality symmetries previously discussed in the
context of specific and theory compactifications may be extended to the
special orbifold that characterizes realistic free-fermion
models.Comment: 15 pages. Standard Late
Phenomenology of Non-Abelian Flat Directions in a Minimal Superstring Standard Model
Recently, we presented the first non-Abelian flat directions that produce
from a heterotic string model solely the three-generation MSSM states as the
massless spectrum in the observable sector of the low energy effective field
theory. In this paper we continue to develop the systematic techniques for the
analysis of nonrenormalizable superpotential terms and non-Abelian flat
direction in realistic string models. Some of our non-Abelian directions were
F-flat to all finite orders in the superpotential. We study for the same string
model the varying phenomenologies resulting from a large set of such all-order
flat directions. We focus on the quark, charged lepton, and Higgs doublet mass
matrices resulting for our phenomenologically superior non-Abelian flat
direction. We review and apply a string-related method for generating large
mass hierarchies between MSSM generations, first discussed in string-derived
flipped SU(5) models, when all generational mass terms are of renormalizable or
very low non-renormalizable order
Classification of the chiral Z2XZ2 fermionic models in the heterotic superstring
The first particle physics observable whose origin may be sought in string
theory is the triple replication of the matter generations. The class of Z2XZ2
orbifolds of six dimensional compactified tori, that have been most widely
studied in the free fermionic formulation, correlate the family triplication
with the existence of three twisted sectors in this class. In this work we seek
an improved understanding of the geometrical origin of the three generation
free fermionic models. Using fermionic and orbifold techniques we classify the
Z2XZ2 orbifold with symmetric shifts on six dimensional compactified internal
manifolds. We show that perturbative three generation models are not obtained
in the case of Z2XZ2 orbifolds with symmetric shifts on complex tori, and that
the perturbative three generation models in this class necessarily employ an
asymmetric shift. We present a class of three generation models in which the
SO(10) gauge symmetry cannot be broken perturbatively, while preserving the
Standard Model matter content. We discuss the potential implications of the
asymmetric shift for strong-weak coupling duality and moduli stabilization. We
show that the freedom in the modular invariant phases in the N=1 vacua that
control the chiral content, can be interpreted as vacuum expectation values of
background fields of the underlying N=4 theory, whose dynamical components are
projected out by the Z2-fermionic projections. In this class of vacua the
chiral content of the models is determined by the underlying N=4 mother theory.Comment: 36 pages. Standard LaTe
- …