156 research outputs found
The Particle Spectrum of Heterotic Compactifications
Techniques are presented for computing the cohomology of stable, holomorphic
vector bundles over elliptically fibered Calabi-Yau threefolds. These
cohomology groups explicitly determine the spectrum of the low energy,
four-dimensional theory. Generic points in vector bundle moduli space manifest
an identical spectrum. However, it is shown that on subsets of moduli space of
co-dimension one or higher, the spectrum can abruptly jump to many different
values. Both analytic and numerical data illustrating this phenomenon are
presented. This result opens the possibility of tunneling or phase transitions
between different particle spectra in the same heterotic compactification. In
the course of this discussion, a classification of SU(5) GUT theories within a
specific context is presented.Comment: 77 pages, 3 figure
The Moduli of Reducible Vector Bundles
A procedure for computing the dimensions of the moduli spaces of reducible,
holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds X is
presented. This procedure is applied to poly-stable rank n+m bundles of the
form V + pi* M, where V is a stable vector bundle with structure group SU(n) on
X and M is a stable vector bundle with structure group SU(m) on the base
surface B of X. Such bundles arise from small instanton transitions involving
five-branes wrapped on fibers of the elliptic fibration. The structure and
physical meaning of these transitions are discussed.Comment: 33+1 page
Yukawa Couplings in Heterotic Standard Models
In this paper, we present a formalism for computing the Yukawa couplings in
heterotic standard models. This is accomplished by calculating the relevant
triple products of cohomology groups, leading to terms proportional to Q*H*u,
Q*Hbar*d, L*H*nu and L*Hbar*e in the low energy superpotential. These
interactions are subject to two very restrictive selection rules arising from
the geometry of the Calabi-Yau manifold. We apply our formalism to the
"minimal" heterotic standard model whose observable sector matter spectrum is
exactly that of the MSSM. The non-vanishing Yukawa interactions are explicitly
computed in this context. These interactions exhibit a texture rendering one
out of the three quark/lepton families naturally light.Comment: 21 pages, LaTe
Heterotic Standard Model Moduli
In previous papers, we introduced a heterotic standard model and discussed
its basic properties. The Calabi-Yau threefold has, generically, three Kahler
and three complex structure moduli. The observable sector of this vacuum has
the spectrum of the MSSM with one additional pair of Higgs-Higgs conjugate
fields. The hidden sector has no charged matter in the strongly coupled string
and only minimal matter for weak coupling. Additionally, the spectrum of both
sectors will contain vector bundle moduli. The exact number of such moduli was
conjectured to be small, but was not explicitly computed. In this paper, we
rectify this and present a formalism for computing the number of vector bundle
moduli. Using this formalism, the number of moduli in both the observable and
strongly coupled hidden sectors is explicitly calculated.Comment: 28 pages, LaTeX; v2: typos corrected, references added; v3:
clarifications, references adde
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
Stability of the Minimal Heterotic Standard Model Bundle
The observable sector of the "minimal heterotic standard model" has precisely
the matter spectrum of the MSSM: three families of quarks and leptons, each
with a right-handed neutrino, and one Higgs-Higgs conjugate pair. In this
paper, it is explicitly proven that the SU(4) holomorphic vector bundle leading
to the MSSM spectrum in the observable sector is slope-stable.Comment: LaTeX, 19 page
Lectures on F-theory compactifications and model building
These lecture notes are devoted to formal and phenomenological aspects of
F-theory. We begin with a pedagogical introduction to the general concepts of
F-theory, covering classic topics such as the connection to Type IIB
orientifolds, the geometry of elliptic fibrations and the emergence of gauge
groups, matter and Yukawa couplings. As a suitable framework for the
construction of compact F-theory vacua we describe a special class of
Weierstrass models called Tate models, whose local properties are captured by
the spectral cover construction. Armed with this technology we proceed with a
survey of F-theory GUT models, aiming at an overview of basic conceptual and
phenomenological aspects, in particular in connection with GUT breaking via
hypercharge flux.Comment: Invited contribution to the proceedings of the CERN Winter School on
Supergravity, Strings and Gauge Theory 2010, to appear in Classical and
Quantum Gravity; 63 pages; v2: references added, typos correcte
Higgs Multiplets in Heterotic GUT Models
For supersymmetric GUT models from heterotic string theory, built from a
stable holomorphic SU(n) vector bundle on a Calabi-Yau threefold , the
net amount of chiral matter can be computed by a Chern class computation.
Corresponding computations for the number of Higgses lead for the
phenomenologically relevant cases of GUT group SU(5) or SO(10) to consideration
of the bundle \La^2 V. In a class of bundles where everything can be computed
explicitly (spectral bundles on elliptic ) we find that the computation for
gives a result which is in conflict with expectations. We argue that this
discrepancy has its origin in the subtle geometry of the spectral data for
\La^2 V and that taking this subtlety into account properly should resolve
the problem.Comment: 29 pages; comments and references adde
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
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