73 research outputs found
Why Does Inflation Start at the Top of the Hill?
We show why the universe started in an unstable de Sitter state. The quantum
origin of our universe implies one must take a `top down' approach to the
problem of initial conditions in cosmology, in which the histories that
contribute to the path integral, depend on the observable being measured. Using
the no boundary proposal to specify the class of histories, we study the
quantum cosmological origin of an inflationary universe in theories like trace
anomaly driven inflation in which the effective potential has a local maximum.
We find that an expanding universe is most likely to emerge in an unstable de
Sitter state, by semiclassical tunneling via a Hawking-Moss instanton. Since
the top down view is forced upon us by the quantum nature of the universe, we
argue that the approach developed here should still apply when the framework of
quantum cosmology will be based on M-Theory.Comment: 21 pages, 1 figur
Duality Versus Supersymmetry and Compactification
We study the interplay between T-duality, compactification and supersymmetry.
We prove that when the original configuration has unbroken space-time
supersymmetries, the dual configuration also does if a special condition is
met: the Killing spinors of the original configuration have to be independent
on the coordinate which corresponds to the isometry direction of the bosonic
fields used for duality. Examples of ``losers" (T-duals are not supersymmetric)
and ``winners" (T-duals are supersymmetric) are given.Comment: LaTeX file, 19 pages, U. of Groningen Report UG-8/94, Stanford U.
Report SU-ITP-94-19, QMW College Report QMW-PH-94-1
Families of N=2 Strings
In a given 4d spacetime bakcground, one can often construct not one but a
family of distinct N=2 string theories. This is due to the multiple ways N=2
superconformal algebra can be embedded in a given worldsheet theory. We
formulate the principle of obtaining different physical theories by gauging
different embeddings of the same symmetry algebra in the same ``pre-theory.''
We then apply it to N=2 strings and formulate the recipe for finding the
associated parameter spaces of gauging. Flat and curved target spaces of both
(4,0) and (2,2) signatures are considered. We broadly divide the gauging
choices into two classes, denoted by alpha and beta, and show them to be
related by T-duality. The distinction between them is formulated topologically
and hinges on some unique properties of 4d manifolds. We determine what their
parameter spaces of gauging are under certain simplicity ansatz for generic
flat spaces (R^4 and its toroidal compactifications) as well as some curved
spaces. We briefly discuss the spectra of D-branes for both alpha and beta
families.Comment: 66+1 pages, 2 tables, latex 2e, hyperref. ver2: typos corrected,
reference adde
Cosmological Evolution of the Rolling Tachyon
The cosmological effects of the tachyon rolling down to its ground state are
discussed by coupling a simple effective field theory for the tachyon field to
Einstein gravity. As the tachyon rolls down to the minimum of its potential the
universe expands. Depending upon initial conditions, the scale factor may or
may not start off accelerating, but ultimately it ceases to do so and the final
flat spacetime is either static in the rest frame of the tachyon (if ) or
(if ) given by the Milne model.Comment: 6 pages, no figures, typos corrected and two refs inserte
A Note on Flux Induced Superpotentials in String Theory
Non-vanishing fluxes in M-theory and string theory compactifications induce a
superpotential in the lower dimensional theory. Gukov has conjectured the
explicit form of this superpotential. We check this conjecture for the
heterotic string compactified on a Calabi-Yau three-fold as well as for warped
M-theory compactifications on Spin(7) holonomy manifolds, by performing a
Kaluza-Klein reduction.Comment: 19 pages, no figure
Preceding rule induction with instance reduction methods
A new prepruning technique for rule induction is presented which applies instance reduction before rule induction. An empirical evaluation records the predictive accuracy and size of rule-sets generated from 24 datasets from the UCI Machine Learning Repository. Three instance reduction algorithms (Edited Nearest Neighbour, AllKnn and DROP5) are compared. Each one is used to reduce the size of the training set, prior to inducing a set of rules using Clark and Boswell's modification of CN2. A hybrid instance reduction algorithm (comprised of AllKnn and DROP5) is also tested. For most of the datasets, pruning the training set using ENN, AllKnn or the hybrid significantly reduces the number of rules generated by CN2, without adversely affecting the predictive performance. The hybrid achieves the highest average predictive accuracy
Holonomy groups and W-symmetries
Irreducible sigma models, i.e. those for which the partition function does
not factorise, are defined on Riemannian spaces with irreducible holonomy
groups. These special geometries are characterised by the existence of
covariantly constant forms which in turn give rise to symmetries of the
supersymmetric sigma model actions. The Poisson bracket algebra of the
corresponding currents is a W-algebra. Extended supersymmetries arise as
special cases.Comment: pages 2
HKT and OKT Geometries on Soliton Black Hole Moduli Spaces
We consider Shiraishi's metrics on the moduli space of extreme black holes.
We interpret the simplification in the pattern of N-body interactions that he
observed in terms of the recent picture of black holes in four and five
dimensions as composites, made up of intersecting branes. We then show that the
geometry of the moduli space of a class of black holes in five and nine
dimensions is hyper-K\"ahler with torsion, and octonionic-K\"ahler with
torsion, respectively. For this, we examine the geometry of point particle
models with extended world-line supersymmetry and show that both of the above
geometries arise naturally in this context. In addition, we construct a large
class of hyper-K\"ahler with torsion and octonionic-K\"ahler with torsion
geometries in various dimensions. We also present a brane interpretation of our
results.Comment: pages 55, phyzzx, some more references have been adde
NS5-Branes, T-Duality and Worldsheet Instantons
The equivalence of NS5-branes and ALF spaces under T-duality is well known.
However, a naive application of T-duality transforms the ALF space into a
smeared NS5-brane, de-localized on the dual, transverse, circle. In this paper
we re-examine this duality, starting from a two-dimensional N=(4,4) gauged
linear sigma model describing Taub-NUT space. After dualizing the circle fiber,
we find that the smeared NS5-brane target space metric receives corrections
from multi-worldsheet instantons. These instantons are identified as
Nielsen-Olesen vortices. We show that their effect is to break the isometry of
the target space, localizing the NS5-brane at a point. The contribution from
the k-instanton sector is shown to be proportional to the weighted integral of
the Euler form over the k-vortex moduli space. The duality also predicts the,
previously unknown, asymptotic exponential decay coefficient of the BPS vortex
solution.Comment: 26 pages. v2: Fourier modes of multi-vortex fermion zero mode
corrected. Reference added. v3: typo correcte
D-Brane Probes of Special Holonomy Manifolds
Using D2-brane probes, we study various properties of M-theory on singular,
non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of
N=1 supersymmetric three-dimensional gauge theories, and apply this technique
to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of
the D2-brane world-volume theory. We derive a ``G_2 quotient construction'' of
non-compact manifolds which admit a metric of G_2 holonomy. We further discuss
the moduli space of such manifolds, including the structure of geometrical
transitions in each case. For completeness, we also include familiar examples
of manifolds with SU(3) and Sp(2) holonomy, where some of the new ideas are
clarified and tested.Comment: 79 pages, Late
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