1,093 research outputs found
On the Connectedness of the Moduli Space of Calabi--Yau Manifolds
We show that the moduli space of all Calabi-Yau manifolds that can be
realized as hypersurfaces described by a transverse polynomial in a four
dimensional weighted projective space, is connected. This is achieved by
exploiting techniques of toric geometry and the construction of Batyrev that
relate Calabi-Yau manifolds to reflexive polyhedra. Taken together with the
previously known fact that the moduli space of all CICY's is connected, and is
moreover connected to the moduli space of the present class of Calabi-Yau
manifolds (since the quintic threefold P_4[5] is both CICY and a hypersurface
in a weighted P_4, this strongly suggests that the moduli space of all simply
connected Calabi-Yau manifolds is connected. It is of interest that singular
Calabi-Yau manifolds corresponding to the points in which the moduli spaces
meet are often, for the present class, more singular than the conifolds that
connect the moduli spaces of CICY's.Comment: 22 pages plain TeX, Tables and references adde
Type B Topological Matter, Kodaira-Spencer Theory, and Mirror Symmetry
Perturbing usual type B topological matter with vector -forms we find
a topological theory which contains explicitly Kodaira-Spencer deformation
theory. It is shown that, in genus zero, three-point correlation functions give
the Yukawa couplings for a generic point in the moduli space of complex
structures. This generalization of type B topological matter seems to be the
correct framework to understand mirror symmetry in terms of two-dimensional
topological field theories.Comment: 17 pages, phyzzx, US-FT/7-9
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
Conifold Transitions and Mirror Symmetries
Recent work initiated by Strominger has lead to a consistent physical
interpretation of certain types of transitions between different string vacua.
These transitions, discovered several years ago, involve singular conifold
configurations which connect distinct Calabi-Yau manifolds. In this paper we
discuss a number of aspects of conifold transitions pertinent to both
worldsheet and spacetime mirror symmetry. It is shown that the mirror transform
based on fractional transformations allows an extension of the mirror map to
conifold boundary points of the moduli space of weighted Calabi-Yau manifolds.
The conifold points encountered in the mirror context are not amenable to an
analysis via the original splitting constructions. We describe the first
examples of such nonsplitting conifold transitions, which turn out to connect
the known web of Calabi-Yau spaces to new regions of the collective moduli
space. We then generalize the splitting conifold transition to weighted
manifolds and describe a class of connections between the webs of ordinary and
weighted projective Calabi-Yau spaces. Combining these two constructions we
find evidence for a dual analog of conifold transitions in heterotic N2
compactifications on K3T and in particular describe the first
conifold transition of a Calabi-Yau manifold whose heterotic dual has been
identified by Kachru and Vafa. We furthermore present a special type of
conifold transition which, when applied to certain classes of Calabi-Yau K3
fibrations, preserves the fiber structure.Comment: 23 page
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
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
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
Quantum fields and "Big Rip" expansion singularities
The effects of quantized conformally invariant massless fields on the
evolution of cosmological models containing a ``Big Rip'' future expansion
singularity are examined. Quantized scalar, spinor, and vector fields are found
to strengthen the accelerating expansion of such models as they approach the
expansion singularity.Comment: 7 pages; REVTeX
One-loop effective multi-gluon Lagrangian in arbitrary dimensions
We exhibit the one-loop multi-gluon effective Lagrangian in any dimension for
a field theory with a quasilocal background, using the background-field
formalism. Specific results, including counter terms (up to 12 spacetime
dimensions), have been derived, applied to the Yang-Mills theory and found to
be in agreement with other string-inspired approaches.Comment: 16 pages, LaTe
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
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