3,396 research outputs found
Puzzles on the Duality between Heterotic and Type IIA Strings
We discuss the possibility of the extension of the duality between the webs
of heterotic string and the type IIA string to Calabi-Yau 3-folds with another
K3 fiber by comparing the dual polyhedron of Calabi-Yau 3-folds given by
Candelas, Perevalov and Rajesh.Comment: Latex, 12 pages, Replacement: solution to puzzles was added, i.e.,
double K3 fibration
Critical Strings from Noncritical Dimensions: A Framework for Mirrors of Rigid Vacau
The role in string theory of manifolds of complex dimension and positive first Chern class is described. In order to be useful for
string theory, the first Chern class of these spaces has to satisfy a certain
relation. Because of this condition the cohomology groups of such manifolds
show a specific structure. A group that is particularly important is described
by --forms because it is this group which contains the
higher dimensional counterpart of the holomorphic --form that
figures so prominently in Calabi--Yau manifolds. It is shown that the higher
dimensional manifolds do not, in general, have a unique counterpart of this
holomorphic form of rank . It is also shown that these manifolds
lead, in general, to a number of additional modes beyond the standard
Calabi--Yau spectrum. This suggests that not only the dilaton but also the
other massless string modes, such as the antisymmetric torsion field, might be
relevant for a possible stringy interpretation.Comment: 7 pages, NSF-ITP-93-3
On Semi-Periods
The periods of the three-form on a Calabi-Yau manifold are found as solutions
of the Picard-Fuchs equations; however, the toric varietal method leads to a
generalized hypergeometric system of equations which has more solutions than
just the periods. This same extended set of equations can be derived from
symmetry considerations. Semi-periods are solutions of this extended system.
They are obtained by integration of the three-form over chains; these chains
can be used to construct cycles which, when integrated over, give periods. In
simple examples we are able to obtain the complete set of solutions for the
extended system. We also conjecture that a certain modification of the method
will generate the full space of solutions in general.Comment: 18 pages, plain TeX. Revised derivation of system of
equations; version to appear in Nuclear Physics
Scaling Behavior in String Theory
In Calabi--Yau compactifications of the heterotic string there exist
quantities which are universal in the sense that they are present in every
Calabi--Yau string vacuum. It is shown that such universal characteristics
provide numerical information, in the form of scaling exponents, about the
space of ground states in string theory. The focus is on two physical
quantities. The first is the Yukawa coupling of a particular antigeneration,
induced in four dimensions by virtue of supersymmetry. The second is the
partition function of the topological sector of the theory, evaluated on the
genus one worldsheet, a quantity relevant for quantum mirror symmetry and
threshold corrections. It is shown that both these quantities exhibit scaling
behavior with respect to a new scaling variable and that a scaling relation
exists between them as well.Comment: 10pp, 4 eps figures (essential
A Stringy Test of the Fate of the Conifold
By studying string loop corrections to superpotential of type II strings
compactified on Calabi-Yau threefolds we find a quantum stringy test and a
confirmation of a recent proposal of Strominger on the fate of the conifold
singularity. We also propose a connection between the spectrum of Bogomolnyi
saturated solitons and one-loop string partition function of topological
strings.Comment: 12 page
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
Exact Results for N=2 Compactifications of Heterotic Strings
We search for , theories which can be realized both as heterotic
string compactifications on and as type II string
compactifications on Calabi-Yau threefolds. In such cases, the exact
non-perturbative superpotential of one string theory is given in terms of tree
level computations in the other string theory. In particular we find concrete
examples which provide the stringy realization of the results of Seiberg and
Witten on N=2 Yang-Mills theory, corrected by gravitational/stringy effects. We
also discuss some examples which shed light on how the moduli spaces of
different N=2 heterotic vacua are connected.Comment: 30 pages, Expansions and Modifications on more potential dual pairs
involving K3 fibrations. Version to appear in Nuclear Physics
A Three-Generation Calabi-Yau Manifold with Small Hodge Numbers
We present a complete intersection Calabi-Yau manifold Y that has Euler
number -72 and which admits free actions by two groups of automorphisms of
order 12. These are the cyclic group Z_12 and the non-Abelian dicyclic group
Dic_3. The quotient manifolds have chi=-6 and Hodge numbers (h^11,h^21)=(1,4).
With the standard embedding of the spin connection in the gauge group, Y gives
rise to an E_6 gauge theory with 3 chiral generations of particles. The gauge
group may be broken further by means of the Hosotani mechanism combined with
continuous deformation of the background gauge field. For the non-Abelian
quotient we obtain a model with 3 generations with the gauge group broken to
that of the standard model. Moreover there is a limit in which the quotients
develop 3 conifold points. These singularities may be resolved simultaneously
to give another manifold with (h^11,h^21)=(2,2) that lies right at the tip of
the distribution of Calabi-Yau manifolds. This strongly suggests that there is
a heterotic vacuum for this manifold that derives from the 3 generation model
on the quotient of Y. The manifold Y may also be realised as a hypersurface in
the toric variety. The symmetry group does not act torically, nevertheless we
are able to identify the mirror of the quotient manifold by adapting the
construction of Batyrev.Comment: PDFLaTeX. 50 pages, 9 figures, 7 table
On Periods for String Compactifications
Motivated by recent developments in the computation of periods for string
compactifications with , we develop a complementary method which also
produces a convenient basis for related calculations. The models are realized
as Calabi--Yau hypersurfaces in weighted projective spaces of dimension four or
as Landau-Ginzburg vacua. The calculation reproduces known results and also
allows a treatment of Landau--Ginzburg orbifolds with more than five fields.Comment: HUPAPP-93/6, IASSNS-HEP-93/80, UTTG-27-93. 21 pages,harvma
Max Kreuzer's Contributions to the Study of Calabi-Yau Manifolds
This is a somewhat personal account of the contributions of Max Kreuzer to
the study of Calabi-Yau manifolds and has been prepared as a contribution to
the Memorial Volume: Strings, Gauge Fields, and the Geometry Behind - The
Legacy of Maximilian Kreuzer, to be published by World Scientific.Comment: 11 pages, pdflatex with pdf figure
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