309 research outputs found
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
Heterotic Gauge Structure of Type II K3 Fibrations
We show that certain classes of K3 fibered Calabi-Yau manifolds derive from
orbifolds of global products of K3 surfaces and particular types of curves.
This observation explains why the gauge groups of the heterotic duals are
determined by the structure of a single K3 surface and provides the dual
heterotic picture of conifold transitions between K3 fibrations. Abstracting
our construction from the special case of K3 hypersurfaces to general K3
manifolds with an appropriate automorphism, we show how to construct Calabi-Yau
threefold duals for heterotic theories with arbitrary gauge groups. This
generalization reveals that the previous limit on the Euler number of
Calabi-Yau manifolds is an artifact of the restriction to the framework of
hypersurfaces.Comment: 15 pages, 3 eps figure
Complex Multiplication of Exactly Solvable Calabi-Yau Varieties
We propose a conceptual framework that leads to an abstract characterization
for the exact solvability of Calabi-Yau varieties in terms of abelian varieties
with complex multiplication. The abelian manifolds are derived from the
cohomology of the Calabi-Yau manifold, and the conformal field theoretic
quantities of the underlying string emerge from the number theoretic structure
induced on the varieties by the complex multiplication symmetry. The geometric
structure that provides a conceptual interpretation of the relation between
geometry and the conformal field theory is discrete, and turns out to be given
by the torsion points on the abelian varieties.Comment: 44 page
Black Hole Attractor Varieties and Complex Multiplication
Black holes in string theory compactified on Calabi-Yau varieties a priori
might be expected to have moduli dependent features. For example the entropy of
the black hole might be expected to depend on the complex structure of the
manifold. This would be inconsistent with known properties of black holes.
Supersymmetric black holes appear to evade this inconsistency by having moduli
fields that flow to fixed points in the moduli space that depend only on the
charges of the black hole. Moore observed in the case of compactifications with
elliptic curve factors that these fixed points are arithmetic, corresponding to
curves with complex multiplication. The main goal of this talk is to explore
the possibility of generalizing such a characterization to Calabi-Yau varieties
with finite fundamental groups.Comment: 21 page
Landau-Ginzburg Vacua of String, M- and F-Theory at c=12
Theories in more than ten dimensions play an important role in understanding
nonperturbative aspects of string theory. Consistent compactifications of such
theories can be constructed via Calabi-Yau fourfolds. These models can be
analyzed particularly efficiently in the Landau-Ginzburg phase of the linear
sigma model, when available. In the present paper we focus on those sigma
models which have both a Landau-Ginzburg phase and a geometric phase described
by hypersurfaces in weighted projective five-space. We describe some of the
pertinent properties of these models, such as the cohomology, the connectivity
of the resulting moduli space, and mirror symmetry among the 1,100,055
configurations which we have constructed.Comment: LaTeX, 33 pages, 10 PostScript figures using epsfig and psfi
A Note On ADE String Compactifications
We address the question whether so-called m-invariants of the N=2 super
Virasoro algebra can be used for the construction of reasonable
four-dimensional string models. It turns out that an infinite subset of those
are pathological in the sense that - although N=2 supersymmetric - the Ramond
sector is not isomorphic to the Neveu-Schwarz sector. Consequently, these two
properties are independent and only requiring both guarantees an N=1 space-time
supersymmetric string spectrum. However, the remaining 529 consistent spectra -
210 of them are mirrors of Gepner models and 76 real orbifolds - show exact
mirror symmetry and are contained in a recent classification of orbifolds of
Gepner models.Comment: 11 pages, plain TeX, no postscript figure
Scaling behavior of observables as a model characteristic in multifield inflation
One of the fundamental questions in inflation is how to characterize the
structure of different types of models in the field theoretic landscape.
Proposals in this direction include attempts to directly characterize the
formal structure of the theory by considering complexity measures of the
potentials. An alternative intrinsic approach is to focus on the behavior of
the observables that result from different models and to ask whether their
behavior differs among models. This type of analysis can be applied even to
nontrivial multifield theories where a natural measure of the complexity of the
model is not obvious and the analytical evaluation of the observables is often
impossible. In such cases one may still compute these observables numerically
and investigate their behavior. One interesting case is when observables show a
scaling behavior, in which case theories can be characterized in terms of their
scaling amplitudes and exponents. Generically, models have nontrivial parameter
spaces, leading to exponents that are functions of these parameters. In such
cases we consider an iterative procedure to determine whether the exponent
functions in turn lead to a scaling behavior. We show that modular inflation
models can be characterized by families of simple scaling laws and that the
scaling exponents that arise in this way in turn show a scaling law in
dependence of these varying energy scales.Comment: 20 pages, 6 figure
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