35,942 research outputs found
Heterotic Line Bundle Standard Models
In a previous publication, arXiv:1106.4804, we have found 200 models from
heterotic Calabi-Yau compactifications with line bundles, which lead to
standard models after taking appropriate quotients by a discrete symmetry and
introducing Wilson lines. In this paper, we construct the resulting standard
models explicitly, compute their spectrum including Higgs multiplets, and
analyze some of their basic properties. After removing redundancies we find
about 400 downstairs models, each with the precise matter spectrum of the
supersymmetric standard model, with one, two or three pairs of Higgs doublets
and no exotics of any kind. In addition to the standard model gauge group, up
to four Green-Schwarz anomalous U(1) symmetries are present in these models,
which constrain the allowed operators in the four-dimensional effective
supergravity. The vector bosons associated to these anomalous U(1) symmetries
are massive. We explicitly compute the spectrum of allowed operators for each
model and present the results, together with the defining data of the models,
in a database of standard models accessible at
http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/linebundlemodels/index.html.
Based on these results we analyze elementary phenomenological properties. For
example, for about 200 models all dimension four and five proton decay
violating operators are forbidden by the additional U(1) symmetries.Comment: 55 pages, Latex, 3 pdf figure
Quiver Structure of Heterotic Moduli
We analyse the vector bundle moduli arising from generic heterotic
compactifications from the point of view of quiver representations. Phenomena
such as stability walls, crossing between chambers of supersymmetry, splitting
of non-Abelian bundles and dynamic generation of D-terms are succinctly encoded
into finite quivers. By studying the Poincar\'e polynomial of the quiver moduli
space using the Reineke formula, we can learn about such useful concepts as
Donaldson-Thomas invariants, instanton transitions and supersymmetry breaking.Comment: 38 pages, 5 figures, 1 tabl
Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds
We systematically approach the construction of heterotic E_8 X E_8 Calabi-Yau
models, based on compact Calabi-Yau three-folds arising from toric geometry and
vector bundles on these manifolds. We focus on a simple class of 101 such
three-folds with smooth ambient spaces, on which we perform an exhaustive scan
and find all positive monad bundles with SU(N), N=3,4,5 structure groups,
subject to the heterotic anomaly cancellation constraint. We find that
anomaly-free positive monads exist on only 11 of these toric three-folds with a
total number of bundles of about 2000. Only 21 of these models, all of them on
three-folds realizable as hypersurfaces in products of projective spaces, allow
for three families of quarks and leptons. We also perform a preliminary scan
over the much larger class of semi-positive monads which leads to about 44000
bundles with 280 of them satisfying the three-family constraint. These 280
models provide a starting point for heterotic model building based on toric
three-folds.Comment: 41 pages, 5 figures. A table modified and a table adde
Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua
In this paper, we show that the presence of gauge fields in heterotic
Calabi-Yau compacitifications causes the stabilisation of some, or all, of the
complex structure moduli of the Calabi-Yau manifold while maintaining a
Minkowski vacuum. Certain deformations of the Calabi-Yau complex structure,
with all other moduli held fixed, can lead to the gauge bundle becoming
non-holomorphic and, hence, non-supersymmetric. This leads to an F-term
potential which stabilizes the corresponding complex structure moduli. We use
10- and 4-dimensional field theory arguments as well as a derivation based
purely on algebraic geometry to show that this picture is indeed correct. An
explicit example is presented in which a large subset of complex structure
moduli is fixed. We demonstrate that this type of theory can serve as the
hidden sector in heterotic vacua and can co-exist with realistic particle
physics.Comment: 17 pages, Late
Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure
We further develop the numerical algorithm for computing the gauge connection
of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In
particular, recent work on the generalized Donaldson algorithm is extended to
bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the
computation depends only on a one-dimensional ray in the Kahler moduli space,
it can probe slope-stability regardless of the size of h^{1,1}. Suitably
normalized error measures are introduced to quantitatively compare results for
different directions in Kahler moduli space. A significantly improved numerical
integration procedure based on adaptive refinements is described and
implemented. Finally, an efficient numerical check is proposed for determining
whether or not a vector bundle is slope-stable without computing its full
connection.Comment: 38 pages, 10 figure
A parallel multigrid solver for multi-patch Isogeometric Analysis
Isogeometric Analysis (IgA) is a framework for setting up spline-based
discretizations of partial differential equations, which has been introduced
around a decade ago and has gained much attention since then. If large spline
degrees are considered, one obtains the approximation power of a high-order
method, but the number of degrees of freedom behaves like for a low-order
method. One important ingredient to use a discretization with large spline
degree, is a robust and preferably parallelizable solver. While numerical
evidence shows that multigrid solvers with standard smoothers (like Gauss
Seidel) does not perform well if the spline degree is increased, the multigrid
solvers proposed by the authors and their co-workers proved to behave optimal
both in the grid size and the spline degree. In the present paper, the authors
want to show that those solvers are parallelizable and that they scale well in
a parallel environment.Comment: The first author would like to thank the Austrian Science Fund (FWF)
for the financial support through the DK W1214-04, while the second author
was supported by the FWF grant NFN S117-0
Nomenclature for naming loci, alleles, linkage groups and chromosomes to be used in poultry genome publications and databases
International audienc
Heterotic domain wall solutions and SU(3) structure manifolds
We examine compactifications of heterotic string theory on manifolds with
SU(3) structure. In particular, we study N = 1/2 domain wall solutions which
correspond to the perturbative vacua of the 4D, N =1 supersymmetric theories
associated to these compactifications. We extend work which has appeared
previously in the literature in two important regards. Firstly, we include two
additional fluxes which have been, heretofore, omitted in the general analysis
of this situation. This allows for solutions with more general torsion classes
than have previously been found. Secondly, we provide explicit solutions for
the fluxes as a function of the torsion classes. These solutions are
particularly useful in deciding whether equations such as the Bianchi
identities can be solved, in addition to the Killing spinor equations
themselves. Our work can be used to straightforwardly decide whether any given
SU(3) structure on a six-dimensional manifold is associated with a solution to
heterotic string theory. To illustrate how to use these results, we discuss a
number of examples taken from the literature.Comment: 34 pages, minor corrections in second versio
Skeletally Dugundji spaces
We introduce and investigate the class of skeletally Dugundji spaces as a
skeletal analogue of Dugundji space. The main result states that the following
conditions are equivalent for a given space : (i) is skeletally
Dugundji; (ii) Every compactification of is co-absolute to a Dugundji
space; (iii) Every -embedding of the absolute in another space is
strongly -regular; (iv) has a multiplicative lattice in the sense of
Shchepin \cite{s76} consisting of skeletal maps
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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