84 research outputs found
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
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 Model Building: 16 Special Manifolds
We study heterotic model building on 16 specific Calabi-Yau manifolds constructed as hypersurfaces in toric four-folds. These 16 manifolds are the only ones among the more than half a billion manifolds in the Kreuzer-Skarke list with a non-trivial first fundamental group. We classify the line bundle models on these manifolds, both for SU(5) and SO(10) GUTs, which lead to consistent supersymmetric string vacua and have three chiral families. A total of about 29000 models is found, most of them corresponding to SO(10) GUTs. These models constitute a starting point for detailed heterotic model building on Calabi-Yau manifolds in the Kreuzer-Skarke list
Heterotic Bundles on Calabi-Yau Manifolds with Small Picard Number
We undertake a systematic scan of vector bundles over spaces from the largest
database of known Calabi-Yau three-folds, in the context of heterotic string
compactification. Specifically, we construct positive rank five monad bundles
over Calabi-Yau hypersurfaces in toric varieties, with the number of Kahler
moduli equal to one, two, and three and extract physically interesting models.
We select models which can lead to three families of matter after dividing by a
freely-acting discrete symmetry and including Wilson lines. About 2000 such
models on two manifolds are found.Comment: 26 pages, 1 figur
On Free Quotients of Complete Intersection Calabi-Yau Manifolds
In order to find novel examples of non-simply connected Calabi-Yau
threefolds, free quotients of complete intersections in products of projective
spaces are classified by means of a computer search. More precisely, all
automorphisms of the product of projective spaces that descend to a free action
on the Calabi-Yau manifold are identified.Comment: 39 pages, 3 tables, LaTe
The MSSM Spectrum from (0,2)-Deformations of the Heterotic Standard Embedding
We construct supersymmetric compactifications of E_8 \times E_8 heterotic
string theory which realise exactly the massless spectrum of the Minimal
Supersymmetric Standard Model (MSSM) at low energies. The starting point is the
standard embedding on a Calabi-Yau threefold which has Hodge numbers
(h^11,h^21) = (1,4) and fundamental group Z_12, which gives an E_6 grand
unified theory with three net chiral generations. The gauge symmetry is then
broken to that of the standard model by a combination of discrete Wilson lines
and continuous deformation of the gauge bundle. On eight distinct branches of
the moduli space, we find stable bundles with appropriate cohomology groups to
give exactly the massless spectrum of the MSSM.Comment: 37 pages including appendice
Landscape Study of Target Space Duality of (0,2) Heterotic String Models
In the framework of (0,2) gauged linear sigma models, we systematically
generate sets of perturbatively dual heterotic string compactifications. This
target space duality is first derived in non-geometric phases and then
translated to the level of GLSMs and its geometric phases. In a landscape
analysis, we compare the massless chiral spectra and the dimensions of the
moduli spaces. Our study includes geometries given by complete intersections of
hypersurfaces in toric varieties equipped with SU(n) vector bundles defined via
the monad construction.Comment: 40 pages, 6 figure
A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List
Kreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions [1]. These polyhedra describe the singular limits of ambient toric varieties in which Calabi-Yau threefolds can exist as hypersurfaces. In this paper, we review how to extract topological and geometric information about Calabi-Yau threefolds using the toric construction, and we provide, in a companion online database (see http://ânuweb1.âneu.âedu/âcydatabase), a detailed inventory of these quantities which are of interest to physicists. Many of the singular ambient spaces described by the Kreuzer-Skarke list can be smoothed out into multiple distinct toric ambient spaces describing different Calabi-Yau threefolds. We provide a list of the different Calabi-Yau threefolds which can be obtained from each polytope, up to current computational limits. We then give the details of a variety of quantities associated to each of these Calabi-Yau such as Chern classes, intersection numbers, and the KĂ€hler and Mori cones, in addition to the Hodge data. This data forms a useful starting point for a number of physical applications of the Kreuzer-Skarke list
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