6,235 research outputs found
(0,2) Target Space Duality, CICYs and Reflexive Sheaves
It is shown that the recently proposed target space duality for (0,2) models
is not limited to models admitting a Landau-Ginzburg description. By studying
some generic examples it is established for the broader class of vector bundles
over complete intersections in toric varieties. Instead of sharing a common
Landau-Ginzburg locus, a pair of dual models agrees in more general
non-geometric phases. The mathematical tools for treating reflexive sheaves are
provided, as well.Comment: 20 pages, TeX, harvma
Some Features of (0,2) Moduli Space
We discuss some aspects of perturbative Calabi-Yau moduli space. In
particular, we show how models with different data can meet along
various sub-loci in their moduli space. In the simplest examples, the models
differ by the choice of desingularization of a holomorphic V-bundle over the
same resolved Calabi-Yau base while in more complicated examples, even the
smooth Calabi-Yau base manifolds can be topologically distinct. These latter
examples extend and clarify a previous observation which was limited to
singular Calabi-Yau spaces and seem to indicate a multicritical structure in
moduli space. This should have a natural F-theory counterpart in terms of the
moduli space of Calabi-Yau four-folds.Comment: 32 pages, 2 eps figures, harvma
Exploring the Moduli Space of (0,2) Strings
We use an exactly solvable (0,2) supersymmetric conformal field theory with
gauge group SO(10) to investigate the superpotential of the corresponding
classical string vacuum. We provide evidence that the rational point lies in
the Landau-Ginzburg phase of the linear sigma-model and calculate exactly all
three- and four-point functions of the gauge singlets. These couplings already
put severe constraints on the possible flat directions of the superpotential.
Finally, we contemplate about the flat direction related to Kahler deformations
of the underlying linear sigma-model.Comment: 19 pages, plain TeX, 2 postscript figures, epsf include
Dilaton Contact Terms in the Bosonic and Heterotic Strings
Dilaton contact terms in the bosonic and heterotic strings are examined
following the recent work of Distler and Nelson on the bosonic and semirigid
strings. In the bosonic case dilaton two-point functions on the sphere are
calculated as a stepping stone to constructing a `good' coordinate family for
dilaton calculations on higher genus surfaces. It is found that dilaton-dilaton
contact terms are improperly normalized, suggesting that the interpretation of
the dilaton as the first variation of string coupling breaks down when other
dilatons are present. It seems likely that this can be attributed to the
tachyon divergence found in \TCCT. For the heterotic case, it is found that
there is no tachyon divergence and that the dilaton contact terms are properly
normalized. Thus, a dilaton equation analogous to the one in topological
gravity is derived and the interpretation of the dilaton as the string coupling
constant goes through.Comment: 44 pages, Figures now included. This replacement version includes the
7 figures as PostScript files appended to the end and the macros to insert
them into the text. Also some typos in intermediate formulae were correcte
Target Space Duality for (0,2) Compactifications
The moduli spaces of two (0,2) compactifications of the heterotic string can
share the same Landau-Ginzburg model even though at large radius they look
completely different. It was argued that such a pair of (0,2) models might be
connected via a perturbative transition at the Landau-Ginzburg point.
Situations of this kind are studied for some explicit models. By calculating
the exact dimensions of the generic moduli spaces at large radius, strong
indications are found in favor of a different scenario. The two moduli spaces
are isomorphic and complex, K\"ahler and bundle moduli get exchanged.Comment: 22 pages, TeX, harvmac, (minor changes, references added
Aspects of (0,2) Orbifolds and Mirror Symmetry
We study orbifolds of (0,2) models and their relation to (0,2) mirror
symmetry. In the Landau-Ginzburg phase of a (0,2) model the superpotential
features a whole bunch of discrete symmetries, which by quotient action lead to
a variety of consistent (0,2) vacua. We study a few examples in very much
detail. Furthermore, we comment on the application of (0,2) mirror symmetry to
the calculation of Yukawa couplings in the space-time superpotential.Comment: 13 pages, TeX (harvmac, big) with 4 enclosed PostScript figures, one
reference adde
Coclass theory for nilpotent semigroups via their associated algebras
Coclass theory has been a highly successful approach towards the
investigation and classification of finite nilpotent groups. Here we suggest a
similar approach for finite nilpotent semigroups. This differs from the group
theory setting in that we additionally use certain algebras associated to the
considered semigroups. We propose a series of conjectures on our suggested
approach. If these become theorems, then this would reduce the classification
of nilpotent semigroups of a fixed coclass to a finite calculation. Our
conjectures are supported by the classification of nilpotent semigroups of
coclass 0 and 1. Computational experiments suggest that the conjectures also
hold for the nilpotent semigroups of coclass 2 and 3.Comment: 13 pages, 2 figure
Miracle at the Gepner Point
A four-point function of singlets, of interest in elucidating the
moduli space of (0,2) deformations of the quintic string vacuum, is computed
using analytic and numerical methods. The conformal field theory amplitude
satisfies the requisite selection rules and monodromy conditions, but the
integrated string amplitude vanishes. Together with selection rules coming from
the spacetime R-symmetry \dksecond, this demonstrates the flatness of the
gauge-singlet spacetime superpotential through fourth order. Relevance to the
more general program of determining the (0,2) moduli space and superpotential
is discussed.Comment: 10 pages, harvmac. Reference completed
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