72 research outputs found
Non-perturbative Gauge Groups and Local Mirror Symmetry
We analyze D-brane states and their central charges on the resolution of
C^2/Z_n by using local mirror symmetry. There is a point in the moduli space
where all n(n-1)/2 branches of the principal component of the discriminant
locus coincide. We argue that this is the point where compactifications of Type
IIA theory on a K3 manifold containing such a local geometry acquire a
non-perturbative gauge symmetry of the type A_{n-1}. This analysis, which
involves an explicit solution of the GKZ system of the local geometry, explains
how the quantum geometry exhibits all positive roots of A_{n-1} and not just
the simple roots that manifest themselves as the exceptional curves of the
classical geometry. We also make some remarks related to McKay correspondence.Comment: 14 pp, LaTex2
Landau-Ginzburg orbifolds with discrete torsion
We complete the classification of (2,2) vacua that can be constructed from
Landau--Ginzburg models by abelian twists with arbitrary discrete torsions.
Compared to the case without torsion the number of new spectra is surprisingly
small. In contrast to a popular expectation mirror symmetry does not seem to be
related to discrete torsion (at least not in the present compactification
framework): The Berglund-H"ubsch construction naturally extends to orbifolds
with torsion; for more general potentials, on the other hand, the new spectra
neither have nor provide mirror partners in our class of models.Comment: 12 pages, LaTe
F-theory, SO(32) and Toric Geometry
We show that the F-theory dual of the heterotic string with unbroken Spin(32)/Z_2 symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbroken E_8\times E_8 symmetry. By considering particular compactifications with this K3 surface as a fiber, we can reproduce the recently found `record gauge group' in six dimensions and obtain a new `record gauge group' in four dimensions. Our observations relate to the toric diagram for the intersection of components of degenerate fibers and our definition of these objects, which we call `tops', is more general than an earlier definition by Candelas and Font
Searching for K3 Fibrations
We present two methods for studying fibrations of Calabi-Yau manifolds
embedded in toric varieties described by single weight systems. We analyse
184,026 such spaces and identify among them 124,701 which are K3 fibrations. As
some of the weights give rise to two or three distinct types of fibrations, the
total number we find is 167,406. With our methods one can also study elliptic
fibrations of 3-folds and K3 surfaces. We also calculate the Hodge numbers of
the 3-folds obtaining more than three times as many as were previously known.Comment: 21 pages, LaTeX2e, 4 eps figures, uses packages
amssymb,latexsym,cite,epi
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
The web of Calabi-Yau hypersurfaces in toric varieties
Recent results on duality between string theories and connectedness of their
moduli spaces seem to go a long way toward establishing the uniqueness of an
underlying theory. For the large class of Calabi-Yau 3-folds that can be
embedded as hypersurfaces in toric varieties the proof of mathematical
connectedness via singular limits is greatly simplified by using polytopes that
are maximal with respect to certain single or multiple weight systems. We
identify the multiple weight systems occurring in this approach. We show that
all of the corresponding Calabi-Yau manifolds are connected among themselves
and to the web of CICY's. This almost completes the proof of connectedness for
toric Calabi-Yau hypersurfaces.Comment: TeX, epsf.tex; 24 page
String Dualities and Toric Geometry: An Introduction
This note is supposed to be an introduction to those concepts of toric
geometry that are necessary to understand applications in the context of string
and F-theory dualities. The presentation is based on the definition of a toric
variety in terms of homogeneous coordinates, stressing the analogy with
weighted projective spaces. We try to give both intuitive pictures and precise
rules that should enable the reader to work with the concepts presented here.Comment: 17 pages, Latex, 7 figures, invited paper to appear in the special
issue of the Journal of Chaos, Solitons and Fractals on "Superstrings, M, F,
S, ... Theory" (M.S. El Naschie and C. Castro, editors
Localized Tachyons and the g_cl conjecture
We consider C/Z_N and C^2/Z_N orbifolds of heterotic string theories and Z_N
orbifolds of AdS_3. We study theories with N=2 worldsheet superconformal
invariance and construct RG flows. Following Harvey, Kutasov, Martinec and
Moore, we compute g_cl and show that it decreases monotonically along RG flows-
as conjectured by them. For the heterotic string theories, the gauge degrees of
freedom do not contribute to the computation of g_cl.Comment: Corrections and clarifications made, 19 page
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