1,253 research outputs found
Toric complete intersections and weighted projective space
It has been shown by Batyrev and Borisov that nef partitions of reflexive
polyhedra can be used to construct mirror pairs of complete intersection
Calabi--Yau manifolds in toric ambient spaces. We construct a number of such
spaces and compute their cohomological data. We also discuss the relation of
our results to complete intersections in weighted projective spaces and try to
recover them as special cases of the toric construction. As compared to
hypersurfaces, codimension two more than doubles the number of spectra with
. Alltogether we find 87 new (mirror pairs of) Hodge data, mainly
with .Comment: 16 pages, LaTeX2e, error in Hodge data correcte
On the Geometry and Homology of Certain Simple Stratified Varieties
We study certain mild degenerations of algebraic varieties which appear in
the analysis of a large class of supersymmetric theories, including superstring
theory. We analyze Witten's sigma-model and find that the non-transversality of
the superpotential induces a singularization and stratification of the ground
state variety. This stratified variety (the union of the singular ground state
variety and its exo-curve strata) admit homology groups which, excepting the
middle dimension, satisfy the "Kahler package" of requirements, extend the
"flopped" pair of small resolutions to an "(exo)flopped" triple, and is
compatible with mirror symmetry and string theory. Finally, we revisit the
conifold transition as it applies to our formalism.Comment: LaTeX 2e, 18 pages, 4 figure
Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings
We construct a bi-linear form on the periods of Calabi-Yau spaces. These are
used to obtain the prepotentials around conifold singularities in type-II
strings compactified on Calabi-Yau space. The explicit construction of the
bi-linear forms is achieved for the one-moduli models as well as two moduli
models with K3-fibrations where the enhanced gauge symmetry is known to be
observed at conifold locus. We also show how these bi-linear forms are related
with the existence of flat coordinates. We list the resulting prepotentials in
two moduli models around the conifold locus, which contains alpha' corrections
of 4-D N=2 SUSY SU(2) Yang-Mills theory as the stringy effect.Comment: Latex file(34pp), a reference added, typos correcte
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
A Class of String Backgrounds as a Semiclassical Limit of WZW Models
A class of string backgrounds associated with non semi-simple groups is
obtained as a special large level limit of ordinary WZW models. The models have
an integer Virasoro central charge and they include the background recently
studied by Nappi and Witten.Comment: 9 page
On the Geometry of Moduli Space of Vacua in N=2 Supersymmetric Yang-Mills Theory
We consider generic properties of the moduli space of vacua in
supersymmetric Yang--Mills theory recently studied by Seiberg and Witten. We
find, on general grounds, Picard--Fuchs type of differential equations
expressing the existence of a flat holomorphic connection, which for one
parameter (i.e. for gauge group ), are second order equations. In the
case of coupling to gravity (as in string theory), where also ``gravitational''
electric and magnetic monopoles are present, the electric--magnetic S duality,
due to quantum corrections, does not seem any longer to be related to
as for supersymmetric theory.Comment: 10 pgs (TeX with harvmac), POLFIS-TH.07/94, CERN-TH.7384/9
Vacuum field energy and spontaneous emission in anomalously dispersive cavities
Anomalously dispersive cavities, particularly white light cavities, may have
larger bandwidth to finesse ratios than their normally dispersive counterparts.
Partly for this reason, their use has been proposed for use in LIGO-like
gravity wave detectors and in ring-laser gyroscopes. In this paper we analyze
the quantum noise associated with anomalously dispersive cavity modes. The
vacuum field energy associated with a particular cavity mode is proportional to
the cavity-averaged group velocity of that mode. For anomalously dispersive
cavities with group index values between 1 and 0, this means that the total
vacuum field energy associated with a particular cavity mode must exceed . For white light cavities in particular, the group index approaches
zero and the vacuum field energy of a particular spatial mode may be
significantly enhanced. We predict enhanced spontaneous emission rates into
anomalously dispersive cavity modes and broadened laser linewidths when the
linewidth of intracavity emitters is broader than the cavity linewidth.Comment: 9 pages, 4 figure
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
GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
We present a detailed study of the generalized hypergeometric system
introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in
the context of toric geometry. GKZ systems arise naturally in the moduli theory
of Calabi-Yau toric varieties, and play an important role in applications of
the mirror symmetry. We find that the Gr\"obner basis for the so-called toric
ideal determines a finite set of differential operators for the local solutions
of the GKZ system. At the special point called the large radius limit, we find
a close relationship between the principal parts of the operators in the GKZ
system and the intersection ring of a toric variety. As applications, we
analyze general three dimensional hypersurfaces of Fermat and non-Fermat types
with Hodge numbers up to . We also find and analyze several non
Landau-Ginzburg models which are related to singular models.Comment: 55 pages, 3 Postscript figures, harvma
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