48 research outputs found
Cohomology of Line Bundles: Applications
Massless modes of both heterotic and Type II string compactifications on
compact manifolds are determined by vector bundle valued cohomology classes.
Various applications of our recent algorithm for the computation of line bundle
valued cohomology classes over toric varieties are presented. For the heterotic
string, the prime examples are so-called monad constructions on Calabi-Yau
manifolds. In the context of Type II orientifolds, one often needs to compute
equivariant cohomology for line bundles, necessitating us to generalize our
algorithm to this case. Moreover, we exemplify that the different terms in
Batyrev's formula and its generalizations can be given a one-to-one
cohomological interpretation.
This paper is considered the third in the row of arXiv:1003.5217 and
arXiv:1006.2392.Comment: 56 pages, 8 tables, cohomCalg incl. Koszul extension available at
http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg
An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts
Even a cursory inspection of the Hodge plot associated with Calabi-Yau
threefolds that are hypersurfaces in toric varieties reveals striking
structures. These patterns correspond to webs of elliptic-K3 fibrations whose
mirror images are also elliptic-K3 fibrations. Such manifolds arise from
reflexive polytopes that can be cut into two parts along slices corresponding
to the K3 fibers. Any two half-polytopes over a given slice can be combined
into a reflexive polytope. This fact, together with a remarkable relation on
the additivity of Hodge numbers, explains much of the structure of the observed
patterns.Comment: 30 pages, 15 colour figure
(0,2) Deformations of Linear Sigma Models
We study (0,2) deformations of a (2,2) supersymmetric gauged linear sigma
model for a Calabi-Yau hypersurface in a Fano toric variety. In the non-linear
sigma model these correspond to some of the holomorphic deformations of the
tangent bundle on the hypersurface. Combinatorial formulas are given for the
number of these deformations, and we show that these numbers are exchanged by
mirror symmetry in a subclass of the models.Comment: 35 pages; uses xy-fig; typos fixed, acknowledgments adde
Few smooth d-polytopes with n lattice points
We prove that, for fixed n there exist only finitely many embeddings of
Q-factorial toric varieties X into P^n that are induced by a complete linear
system. The proof is based on a combinatorial result that for fixed nonnegative
integers d and n, there are only finitely many smooth d-polytopes with n
lattice points. We also enumerate all smooth 3-polytopes with at most 12
lattice points. In fact, it is sufficient to bound the singularities and the
number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result
On the Hodge structure of elliptically fibered Calabi-Yau threefolds
The Hodge numbers of generic elliptically fibered Calabi-Yau threefolds over
toric base surfaces fill out the "shield" structure previously identified by
Kreuzer and Skarke. The connectivity structure of these spaces and bounds on
the Hodge numbers are illuminated by considerations from F-theory and the
minimal model program. In particular, there is a rigorous bound on the Hodge
number h_{21} <= 491 for any elliptically fibered Calabi-Yau threefold. The
threefolds with the largest known Hodge numbers are associated with a sequence
of blow-ups of toric bases beginning with the Hirzebruch surface F_{12} and
ending with the toric base for the F-theory model with largest known gauge
group.Comment: 16 pages, 4 figures; v2: minor corrections, references added; v3:
minor corrections, improvements, reference added, version for JHE
Deforming, revolving and resolving - New paths in the string theory landscape
In this paper we investigate the properties of series of vacua in the string
theory landscape. In particular, we study minima to the flux potential in type
IIB compactifications on the mirror quintic. Using geometric transitions, we
embed its one dimensional complex structure moduli space in that of another
Calabi-Yau with h^{1,1}=86 and h^{2,1}=2. We then show how to construct
infinite series of continuously connected minima to the mirror quintic
potential by moving into this larger moduli space, applying its monodromies,
and moving back. We provide an example of such series, and discuss their
implications for the string theory landscape.Comment: 41 pages, 5 figures; minor corrections, published versio
The 24-Cell and Calabi-Yau Threefolds with Hodge Numbers (1,1)
Calabi-Yau threefolds with h^11(X)=h^21(X)=1 are constructed as free
quotients of a hypersurface in the ambient toric variety defined by the
24-cell. Their fundamental groups are SL(2,3), a semidirect product of Z_3 and
Z_8, and Z_3 x Q_8.Comment: 22 pages, 3 figures, 3 table
Brane Tilings and Specular Duality
We study a new duality which pairs 4d N=1 supersymmetric quiver gauge
theories. They are represented by brane tilings and are worldvolume theories of
D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies
theories which have the same combined mesonic and baryonic moduli space,
otherwise called the master space. We obtain the associated Hilbert series
which encodes both the generators and defining relations of the moduli space.
We illustrate our findings with a set of brane tilings that have reflexive
toric diagrams.Comment: 42 pages, 16 figures, 5 table
Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
We present the most complete list of mirror pairs of Calabi-Yau complete
intersections in toric ambient varieties and develop the methods to solve the
topological string and to calculate higher genus amplitudes on these compact
Calabi-Yau spaces. These symplectic invariants are used to remove redundancies
in examples. The construction of the B-model propagators leads to compatibility
conditions, which constrain multi-parameter mirror maps. For K3 fibered
Calabi-Yau spaces without reducible fibers we find closed formulas for all
genus contributions in the fiber direction from the geometry of the fibration.
If the heterotic dual to this geometry is known, the higher genus invariants
can be identified with the degeneracies of BPS states contributing to
gravitational threshold corrections and all genus checks on string duality in
the perturbative regime are accomplished. We find, however, that the BPS
degeneracies do not uniquely fix the non-perturbative completion of the
heterotic string. For these geometries we can write the topological partition
function in terms of the Donaldson-Thomas invariants and we perform a
non-trivial check of S-duality in topological strings. We further investigate
transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2
quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur
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