4,036 research outputs found
Yukawa Textures From Heterotic Stability Walls
A holomorphic vector bundle on a Calabi-Yau threefold, X, with h^{1,1}(X)>1
can have regions of its Kahler cone where it is slope-stable, that is, where
the four-dimensional theory is N=1 supersymmetric, bounded by "walls of
stability". On these walls the bundle becomes poly-stable, decomposing into a
direct sum, and the low energy gauge group is enhanced by at least one
anomalous U(1) gauge factor. In this paper, we show that these additional
symmetries can strongly constrain the superpotential in the stable region,
leading to non-trivial textures of Yukawa interactions and restrictions on
allowed masses for vector-like pairs of matter multiplets. The Yukawa textures
exhibit a hierarchy; large couplings arise on the stability wall and some
suppressed interactions "grow back" off the wall, where the extended U(1)
symmetries are spontaneously broken. A number of explicit examples are
presented involving both one and two stability walls, with different
decompositions of the bundle structure group. A three family standard-like
model with no vector-like pairs is given as an example of a class of SU(4)
bundles that has a naturally heavy third quark/lepton family. Finally, we
present the complete set of Yukawa textures that can arise for any holomorphic
bundle with one stability wall where the structure group breaks into two
factors.Comment: 53 pages, 4 figures and 13 table
The B-L/Electroweak Hierarchy in Smooth Heterotic Compactifications
E8 X E8 heterotic string and M-theory, when appropriately compactified, can
give rise to realistic, N=1 supersymmetric particle physics. In particular, the
exact matter spectrum of the MSSM, including three right-handed neutrino
supermultiplets, one per family, and one pair of Higgs-Higgs conjugate
superfields is obtained by compactifying on Calabi-Yau manifolds admitting
specific SU(4) vector bundles. These "heterotic standard models" have the
SU(3)_{C} X SU(2)_{L} X U(1)_{Y} gauge group of the standard model augmented by
an additional gauged U(1)_{B-L}. Their minimal content requires that the B-L
gauge symmetry be spontaneously broken by a vacuum expectation value of at
least one right-handed sneutrino. In a previous paper, we presented the results
of a renormalization group analysis showing that B-L gauge symmetry is indeed
radiatively broken with a B-L/electroweak hierarchy of O(10) to O(10^{2}). In
this paper, we present the details of that analysis, extending the results to
include higher order terms in tan[beta]^{-1} and the explicit spectrum of all
squarks and sleptons.Comment: 60 pages, 6 figure
Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories
A numerical algorithm is presented for explicitly computing the gauge
connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds.
To illustrate this algorithm, we calculate the connections on stable monad
bundles defined on the K3 twofold and Quintic threefold. An error measure is
introduced to determine how closely our algorithmic connection approximates a
solution to the Hermitian Yang-Mills equations. We then extend our results by
investigating the behavior of non slope-stable bundles. In a variety of
examples, it is shown that the failure of these bundles to satisfy the
Hermitian Yang-Mills equations, including field-strength singularities, can be
accurately reproduced numerically. These results make it possible to
numerically determine whether or not a vector bundle is slope-stable, thus
providing an important new tool in the exploration of heterotic vacua.Comment: 52 pages, 15 figures. LaTex formatting of figures corrected in
version 2
The B-L/Electroweak Hierarchy in Heterotic String and M-Theory
E8 x E8 heterotic string and M-theory, when compactified on a Calabi-Yau
threefold admitting an SU(4) vector bundle with Wilson lines, can give rise to
the exact MSSM spectrum with three right-handed neutrino chiral superields, one
per family. Rank preserving Wilson lines require that the standard model group
be augmented by a gauged U(1)_B-L. Since there are no fields in this theory for
which 3(B-L) is an even, non-zero integer, the gauged B-L symmetry must be
spontaneously broken at a low scale, not too far above the electroweak scale.
It is shown that in these heterotic standard models, the B-L symmetry can be
broken, with a phenomenologically viable B-L/electroweak hierarchy, by at least
one right-handed sneutrino acquiring a vacuum expectation value. This is
explicitly demonstrated, in a specific region of parameter space, using a
renormalization group analysis and soft supersymmetry breaking operators. The
vacuum state is shown to be a stable, local minimum of the potential and the
resultant hierarchy is explicitly presented in terms of tan[beta].Comment: 16 pages; typos fixed, analysis generalize
The Exact MSSM Spectrum from String Theory
We show the existence of realistic vacua in string theory whose observable
sector has exactly the matter content of the MSSM. This is achieved by
compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau
threefold with an SU(4) gauge instanton and a Z_3 x Z_3 Wilson line.
Specifically, the observable sector is N=1 supersymmetric with gauge group
SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons,
each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair.
Importantly, there are no extra vector-like pairs and no exotic matter in the
zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge
instanton moduli in the observable sector. The holomorphic SU(4) vector bundle
of the observable sector is slope-stable.Comment: 15 pages, LaTeX; v2: Hidden sector is unstable, symbol typesetting
error corrected, clarifications and references added; v3: New discussion of
hidden secto
Stabilizing All Geometric Moduli in Heterotic Calabi-Yau Vacua
We propose a scenario to stabilize all geometric moduli - that is, the
complex structure, Kahler moduli and the dilaton - in smooth heterotic
Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is
accomplished using the gauge bundle required in any heterotic compactification,
whose perturbative effects on the moduli are combined with non-perturbative
corrections. We argue that, for appropriate gauge bundles, all complex
structure and a large number of other moduli can be perturbatively stabilized -
in the most restrictive case, leaving only one combination of Kahler moduli and
the dilaton as a flat direction. At this stage, the remaining moduli space
consists of Minkowski vacua. That is, the perturbative superpotential vanishes
in the vacuum without the necessity to fine-tune flux. Finally, we incorporate
non-perturbative effects such as gaugino condensation and/or instantons. These
are strongly constrained by the anomalous U(1) symmetries which arise from the
required bundle constructions. We present a specific example, with a consistent
choice of non-perturbative effects, where all remaining flat directions are
stabilized in an AdS vacuum.Comment: 24 pages, 2 figure
Wilson Lines and a Canonical Basis of SU(4) Heterotic Standard Models
The spontaneous breaking of SU(4) heterotic standard models by Z_3 x Z_3
Wilson lines to the MSSM with three right-handed neutrino supermultiplets and
gauge group SU(3)_C x SU(2)_L x U(1) x U(1) is explored. The two-dimensional
subspace of the Spin(10) Lie algebra that commutes with su(3)_C + su(2)_L is
analyzed. It is shown that there is a unique basis for which the initial soft
supersymmetry breaking parameters are uncorrelated and for which the U(1) x
U(1) field strengths have no kinetic mixing at any scale. If the Wilson lines
"turn on" at different scales, there is an intermediate regime with either a
left-right or a Pati-Salam type model. We compute their spectra directly from
string theory, and adjust the associated mass parameter so that all gauge
parameters exactly unify. A detailed analysis of the running gauge couplings
and soft gaugino masses is presented.Comment: 59 pages, 9 figure
Stability Walls in Heterotic Theories
We study the sub-structure of the heterotic Kahler moduli space due to the
presence of non-Abelian internal gauge fields from the perspective of the
four-dimensional effective theory. Internal gauge fields can be supersymmetric
in some regions of the Kahler moduli space but break supersymmetry in others.
In the context of the four-dimensional theory, we investigate what happens when
the Kahler moduli are changed from the supersymmetric to the non-supersymmetric
region. Our results provide a low-energy description of supersymmetry breaking
by internal gauge fields as well as a physical picture for the mathematical
notion of bundle stability. Specifically, we find that at the transition
between the two regions an additional anomalous U(1) symmetry appears under
which some of the states in the low-energy theory acquire charges. We compute
the associated D-term contribution to the four-dimensional potential which
contains a Kahler-moduli dependent Fayet-Iliopoulos term and contributions from
the charged states. We show that this D-term correctly reproduces the expected
physics. Several mathematical conclusions concerning vector bundle stability
are drawn from our arguments. We also discuss possible physical applications of
our results to heterotic model building and moduli stabilization.Comment: 37 pages, 4 figure
B-L Cosmic Strings in Heterotic Standard Models
E_{8} X E_{8} heterotic string and M-theory, when compactified on smooth
Calabi-Yau manifolds with SU(4) vector bundles, can give rise to softly broken
N=1 supersymmetric theories with the exact matter spectrum of the MSSM,
including three right-handed neutrinos and one Higgs-Higgs conjugate pair of
supermultiplets. These vacua have the SU(3)_{C} X SU(2)_{L} X U(1)_{Y} gauge
group of the standard model augmented by an additional gauged U(1)_{B-L}. Their
minimal content requires that the B-L symmetry be spontaneously broken by a
vacuum expectation value of at least one right-handed sneutrino. The soft
supersymmetry breaking operators can induce radiative breaking of the B-L gauge
symmetry with an acceptable B-L/electroweak hierarchy. In this paper, it is
shown that U(1)_{B-L} cosmic strings occur in this context, potentially with
both bosonic and fermionic superconductivity. We present a numerical analysis
that demonstrates that boson condensates can, in principle, form for theories
of this type. However, the weak Yukawa and gauge couplings of the right-handed
sneutrino suggests that bosonic superconductivity will not occur in the
simplest vacua in this context. The electroweak phase transition also disallows
fermion superconductivity, although substantial bound state fermion currents
can exist.Comment: 41 pages, 5 figure
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