3,341 research outputs found
Non-principal ultrafilters, program extraction and higher order reverse mathematics
We investigate the strength of the existence of a non-principal ultrafilter
over fragments of higher order arithmetic.
Let U be the statement that a non-principal ultrafilter exists and let
ACA_0^{\omega} be the higher order extension of ACA_0. We show that
ACA_0^{\omega}+U is \Pi^1_2-conservative over ACA_0^{\omega} and thus that
ACA_0^{\omega}+\U is conservative over PA.
Moreover, we provide a program extraction method and show that from a proof
of a strictly \Pi^1_2 statement \forall f \exists g A(f,g) in ACA_0^{\omega}+U
a realizing term in G\"odel's system T can be extracted. This means that one
can extract a term t, such that A(f,t(f))
Superstring BRST Cohomology
We first derive all world-sheet action functionals for NSR superstring models
with (1,1) supersymmetry and any number of abelian gauge fields, for gauge
transformations of the standard form. Then we prove for these models that the
BRST cohomology groups , (with the antifields taken into account)
are isomorphic to those of the corresponding bosonic string models, whose
cohomology is fully known. This implies that the nontrivial global symmetries,
Noether currents, background charges, consistent deformations and candidate
gauge anomalies of an NSR (1,1) superstring model are in one-to-one
correspondence with their bosonic counterparts.Comment: LaTeX2e, 44 pages, minor correction
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
Toric Construction of Global F-Theory GUTs
We systematically construct a large number of compact Calabi-Yau fourfolds
which are suitable for F-theory model building. These elliptically fibered
Calabi-Yaus are complete intersections of two hypersurfaces in a six
dimensional ambient space. We first construct three-dimensional base manifolds
that are hypersurfaces in a toric ambient space. We search for divisors which
can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations
over these base manifolds. We find that elementary conditions which are
motivated by F-theory GUTs lead to strong constraints on the geometry, which
significantly reduce the number of suitable models. The complete database of
models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out
several examples in more detail.Comment: 35 pages, references adde
NS Fivebrane and Tachyon Condensation
We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained
from the condensation of the tachyon on the unstable D9-brane of type IIA
theory. The construction uses a combination of the descriptions of these branes
as solitons of the worldvolume theory of the D9-brane. The NS5-brane, in
particular, involves a gauge bundle which is operator valued, and hence is
better thought of as a gerbe.Comment: 20 pages, harvma
Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds
We systematically approach the construction of heterotic E_8 X E_8 Calabi-Yau
models, based on compact Calabi-Yau three-folds arising from toric geometry and
vector bundles on these manifolds. We focus on a simple class of 101 such
three-folds with smooth ambient spaces, on which we perform an exhaustive scan
and find all positive monad bundles with SU(N), N=3,4,5 structure groups,
subject to the heterotic anomaly cancellation constraint. We find that
anomaly-free positive monads exist on only 11 of these toric three-folds with a
total number of bundles of about 2000. Only 21 of these models, all of them on
three-folds realizable as hypersurfaces in products of projective spaces, allow
for three families of quarks and leptons. We also perform a preliminary scan
over the much larger class of semi-positive monads which leads to about 44000
bundles with 280 of them satisfying the three-family constraint. These 280
models provide a starting point for heterotic model building based on toric
three-folds.Comment: 41 pages, 5 figures. A table modified and a table adde
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