540 research outputs found
De Sitter Space and Spatial Topology
Morrow-Jones and Witt have shown that generic spatial topologies admit
initial data that evolve to locally de Sitter spacetimes under Einstein's
equations. We simplify their arguments, make them a little more general, and
solve for the global time evolution of the wormhole initial data considered by
them. Finally we give explicit examples of locally de Sitter domains of
development whose universal covers cannot be embedded in de Sitter space.Comment: 21 pages, 7 figure
Two universal results for Wilson loops at strong coupling
We present results for Wilson loops in strongly coupled gauge theories. The
loops may be taken around an arbitrarily shaped contour and in any field theory
with a dual IIB geometry of the form M x S^5. No assumptions about
supersymmetry are made. The first result uses D5 branes to show how the loop in
any antisymmetric representation is computed in terms of the loop in the
fundamental representation. The second result uses D3 branes to observe that
each loop defines a rich sequence of operators associated with minimal surfaces
in S^5. The action of these configurations are all computable. Both results
have features suggesting a connection with integrability.Comment: 1+12 pages. LaTeX. No figure
Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity
We further develop on the study of the conditions for the existence of
locally stable non-supersymmetric vacua with vanishing cosmological constant in
supergravity models involving only chiral superfields. Starting from the two
necessary conditions for flatness and stability derived in a previous paper
(which involve the Kahler metric and its Riemann tensor contracted with the
supersymmetry breaking auxiliary fields) we show that the implications of these
constraints can be worked out exactly not only for factorizable scalar
manifolds, but also for symmetric coset manifolds. In both cases, the
conditions imply a strong restriction on the Kahler geometry and constrain the
vector of auxiliary fields defining the Goldstino direction to lie in a certain
cone. We then apply these results to the various homogeneous coset manifolds
spanned by the moduli and untwisted matter fields arising in string
compactifications, and discuss their implications. Finally, we also discuss
what can be said for completely arbitrary scalar manifolds, and derive in this
more general case some explicit but weaker restrictions on the Kahler geometry.Comment: 22 pages, Latex, no figure
Brane Resolution Through Fibration
We consider p-branes with one or more circular directions fibered over the
transverse space. The fibration, in conjunction with the transverse space
having a blown-up cycle, enables these p-brane solutions to be completely
regular. Some such circularly-wrapped D3-brane solutions describe flows from
SU(N)^3 N=2 theory, F_0 theory, as well as an infinite family of superconformal
quiver gauge theories, down to three-dimensional field theories. We discuss the
operators that are turned on away from the UV fixed points. Similarly, there
are wrapped M2-brane solutions which describe smooth flows from known
three-dimensional supersymmetric Chern-Simons matter theories, such as ABJM
theory. We also consider p-brane solutions on gravitational instantons, and
discuss various ways in which U-duality can be applied to yield other
non-singular solutions.Comment: 35 pages, additional referenc
Self-gravitating branes of codimension 4 in Lovelock gravity
We construct a familly of exact solutions of Lovelock equations describing
codimension four branes with discrete symmetry in the transverse space. Unlike
what is known from pure Einstein gravity, where such brane solutions of higher
codimension are singular, the solutions we find, for the complete Lovelock
theory, only present removable singularities. The latter account for a
localised tension-like energy-momentum tensor on the brane, in analogy with the
case of a codimension two self-gravitating cosmic string in pure Einstein
gravity. However, the solutions we discuss present two main distinctive
features : the tension of the brane receives corrections from the induced
curvature of the brane's worldsheet and, in a given Lovelock theory, the
spectrum of possible values of the tension is discrete. These solutions provide
a new framework for the study of higher codimension braneworlds.Comment: 22 page
The Dirichlet and the weighted metrics for the space of Kahler metrics
In this work we study the intrinsic geometry of the space of Kahler metrics
under various Riemannian metrics. The first part is on the Dirichlet metric. We
motivate its study, we compute its curvature, and we make links with the Calabi
metric, the K-energy, the degenerate complex Hessian equation. The second part
is on the weighted metrics, for which we investigate as well their geometric
properties.Comment: 33 pages, new sections on the weighted metric
The -structures on complex line bundles and explicit Riemannian metrics with SU(4)-holonomy
We completely explore the system of ODE's which is equivalent to the
existence of a parallel -structure on the cone over a 7-dimensional
3-Sasakian manifold. The one-dimensional family of solutions of this system is
constructed. The solutions of this family correspond to metrics with holonomy
SU(4) which generalize the Calabi metrics.Comment: 11 page
Self-Duality in D <= 8-dimensional Euclidean Gravity
In the context of D-dimensional Euclidean gravity, we define the natural
generalisation to D-dimensions of the self-dual Yang-Mills equations, as
duality conditions on the curvature 2-form of a Riemannian manifold. Solutions
to these self-duality equations are provided by manifolds of SU(2), SU(3), G_2
and Spin(7) holonomy. The equations in eight dimensions are a master set for
those in lower dimensions. By considering gauge fields propagating on these
self-dual manifolds and embedding the spin connection in the gauge connection,
solutions to the D-dimensional equations for self-dual Yang-Mills fields are
found. We show that the Yang-Mills action on such manifolds is topologically
bounded from below, with the bound saturated precisely when the Yang-Mills
field is self-dual. These results have a natural interpretation in
supersymmetric string theory.Comment: 9 pages, Latex, factors in eqn. (6) corrected, acknowledgement and
reference added, typos fixe
Balanced metrics on Cartan and Cartan-Hartogs domains
This paper consists of two results dealing with balanced metrics (in S.
Donaldson terminology) on nonconpact complex manifolds. In the first one we
describe all balanced metrics on Cartan domains. In the second one we show that
the only Cartan-Hartogs domain which admits a balanced metric is the complex
hyperbolic space. By combining these results with those obtained in [13]
(Kaehler-Einstein submanifolds of the infinite dimensional projective space, to
appear in Mathematische Annalen) we also provide the first example of complete,
Kaehler-Einstein and projectively induced metric g such that is not
balanced for all .Comment: 11 page
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