140,979 research outputs found
On timelike supersymmetric solutions of gauged minimal 5-dimensional supergravity
We analyze the timelike supersymmetric solutions of minimal gauged
5-dimensional supergravity for the case in which the K\"ahler base manifold
admits a holomorphic isometry and depends on two real functions satisfying a
simple second-order differential equation. Using this general form of the base
space, the equations satisfied by the building blocks of the solutions become
of, at most, fourth degree and can be solved by simple polynomic ansatzs. In
this way we construct two 3-parameter families of solutions that contain almost
all the timelike supersymmetric solutions of this theory with one angular
momentum known so far and a few more: the (singular) supersymmetric
Reissner-Nordstr\"om-AdS solutions, the three exact supersymmetric solutions
describing the three near-horizon geometries found by Gutowski and Reall, three
1-parameter asymptotically-AdS black-hole solutions with those three
near-horizon geometries (Gutowski and Reall's black hole being one of them),
three generalizations of the G\"odel universe and a few potentially homogenous
solutions. A key r\^ole in finding these solutions is played by our ability to
write AdS's K\"ahler base space ( or
SUU) is three different, yet simple, forms associated to three
different isometries. Furthermore, our ansatz for the K\"ahler metric also
allows us to study the dimensional compactification of the theory and its
solutions in a systematic way.Comment: 57 pages. References and comments adde
Duality and Fibrations on G_2 Manifolds
We argue that G_2 manifolds for M-theory admitting string theory Calabi-Yau
duals are fibered by coassociative submanifolds. Dual theories are constructed
using the moduli space of M5-brane fibers as target space. Mirror symmetry and
various string and M-theory dualities involving G_2 manifolds may be
incorporated into this framework. To give some examples, we construct two
non-compact manifolds with G_2 structures: one with a K3 fibration, and one
with a torus fibration and a metric of G_2 holonomy. Kaluza-Klein reduction of
the latter solution gives abelian BPS monopoles in 3+1 dimensions.Comment: 40 pages, 2 figures, LaTe
A 4D gravity theory and G2-holonomy manifolds
Bryant and Salamon gave a construction of metrics of G2 holonomy on the total
space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional
self-dual Einstein manifold. We generalise it by considering the total space of
an SO(3) bundle (with fibers R^3) over a 4-dimensional base, with a connection
on this bundle. We make essentially the same ansatz for the calibrating 3-form,
but use the curvature 2-forms instead of the ASD ones. We show that the
resulting 3-form defines a metric of G2 holonomy if the connection satisfies a
certain second-order PDE. This is exactly the same PDE that arises as the field
equation of a certain 4-dimensional gravity theory formulated as a
diffeomorphism-invariant theory of SO(3) connections. Thus, every solution of
this 4-dimensional gravity theory can be lifted to a G2-holonomy metric. Unlike
all previously known constructions, the theory that we lift to 7 dimensions is
not topological. Thus, our construction should give rise to many new metrics of
G2 holonomy. We describe several examples that are of cohomogeneity one on the
base.Comment: 25 page
Orientifolds and Slumps in G_2 and Spin(7) Metrics
We discuss some new metrics of special holonomy, and their roles in string
theory and M-theory. First we consider Spin(7) metrics denoted by C_8, which
are complete on a complex line bundle over CP^3. The principal orbits are S^7,
described as a triaxially squashed S^3 bundle over S^4. The behaviour in the
S^3 directions is similar to that in the Atiyah-Hitchin metric, and we show how
this leads to an M-theory interpretation with orientifold D6-branes wrapped
over S^4. We then consider new G_2 metrics which we denote by C_7, which are
complete on an R^2 bundle over T^{1,1}, with principal orbits that are
S^3\times S^3. We study the C_7 metrics using numerical methods, and we find
that they have the remarkable property of admitting a U(1) Killing vector whose
length is nowhere zero or infinite. This allows one to make an everywhere
non-singular reduction of an M-theory solution to give a solution of the type
IIA theory. The solution has two non-trivial S^2 cycles, and both carry
magnetic charge with respect to the R-R vector field. We also discuss some
four-dimensional hyper-Kahler metrics described recently by Cherkis and
Kapustin, following earlier work by Kronheimer. We show that in certain cases
these metrics, whose explicit form is known only asymptotically, can be related
to metrics characterised by solutions of the su(\infty) Toda equation, which
can provide a way of studying their interior structure.Comment: Latex, 45 pages; minor correction
New Complete Non-compact Spin(7) Manifolds
We construct new explicit metrics on complete non-compact Riemannian
8-manifolds with holonomy Spin(7). One manifold, which we denote by A_8, is
topologically R^8 and another, which we denote by B_8, is the bundle of chiral
spinors over . Unlike the previously-known complete non-compact metric of
Spin(7) holonomy, which was also defined on the bundle of chiral spinors over
S^4, our new metrics are asymptotically locally conical (ALC): near infinity
they approach a circle bundle with fibres of constant length over a cone whose
base is the squashed Einstein metric on CP^3. We construct the
covariantly-constant spinor and calibrating 4-form. We also obtain an
L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of
opposite dualities) for the B_8 manifold. We use the metrics to construct new
supersymmetric brane solutions in M-theory and string theory. In particular, we
construct resolved fractional M2-branes involving the use of the L^2 harmonic
4-forms, and show that for each manifold there is a supersymmetric example. An
intriguing feature of the new A_8 and B_8 Spin(7) metrics is that they are
actually the same local solution, with the two different complete manifolds
corresponding to taking the radial coordinate to be either positive or
negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which
by contrast do not have special holonomy. In an appendix we construct the
general solution of our first-order equations for Spin(7) holonomy, and obtain
further regular metrics that are complete on manifolds B^+_8 and B^-_8 similar
to B_8.Comment: Latex, 29 pages. Appendix obtaining general solution of first-order
equations and additional complete Spin(7) manifolds adde
Compact Einstein Spaces based on Quaternionic K\"ahler Manifolds
We investigate the Einstein equation with a positive cosmological constant
for -dimensional metrics on bundles over Quaternionic K\"ahler base
manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein
equations are reduced to a set of non-linear ordinary differential equations.
We numerically find inhomogeneous compact Einstein spaces with orbifold
singularity.Comment: LaTeX 28 pages, 5 eps figure
Nuttier Bubbles
We construct new explicit solutions of general relativity from double
analytic continuations of Taub-NUT spacetimes. This generalizes previous
studies of 4-dimensional nutty bubbles. One 5-dimensional locally
asymptotically AdS solution in particular has a special conformal boundary
structure of . We compute its boundary stress tensor and
relate it to the properties of the dual field theory. Interestingly enough, we
also find consistent 6-dimensional bubble solutions that have only one timelike
direction. The existence of such spacetimes with non-trivial topology is
closely related to the existence of the Taub-NUT(-AdS) solutions with more than
one NUT charge. Finally, we begin an investigation of generating new solutions
from Taub-NUT spacetimes and nuttier bubbles. Using the so-called Hopf duality,
we provide new explicit time-dependent backgrounds in six dimensions.Comment: 32 pages, 1 figure; v.3. typos corrected. Matches the published
versio
Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)
The classifications of holonomy groups in Lorentzian and in Euclidean
signature are quite different. A group of interest in Lorentzian signature in n
dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2).
Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg,
and a single four-dimensional example with a non-zero cosmological constant was
exhibited by Ghanam and Thompson. Here we reduce the problem of finding the
general -dimensional Einstein metric of SIM(n-2) holonomy, with and without
a cosmological constant, to solving a set linear generalised Laplace and
Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit
examples may be constructed in terms of generalised harmonic functions. A
dimensional reduction of these multi-centre solutions gives new time-dependent
Kaluza-Klein black holes and monopoles, including time-dependent black holes in
a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page
Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
The Eisenhart-Duval lift allows embedding non-relativistic theories into a
Lorentzian geometrical setting. In this paper we study the lift from the point
of view of the Dirac equation and its hidden symmetries. We show that
dimensional reduction of the Dirac equation for the Eisenhart-Duval metric in
general gives rise to the non-relativistic Levy-Leblond equation in lower
dimension. We study in detail in which specific cases the lower dimensional
limit is given by the Dirac equation, with scalar and vector flux, and the
relation between lift, reduction and the hidden symmetries of the Dirac
equation. While there is a precise correspondence in the case of the lower
dimensional massive Dirac equation with no flux, we find that for generic
fluxes it is not possible to lift or reduce all solutions and hidden
symmetries. As a by-product of this analysis we construct new Lorentzian
metrics with special tensors by lifting Killing-Yano and Closed Conformal
Killing-Yano tensors and describe the general Conformal Killing-Yano tensor of
the Eisenhart-Duval lift metrics in terms of lower dimensional forms. Lastly,
we show how dimensionally reducing the higher dimensional operators of the
massless Dirac equation that are associated to shared hidden symmetries it is
possible to recover hidden symmetry operators for the Dirac equation with flux.Comment: 18 pages, no figures. Version 3: some typos corrected, some
discussions clarified, part of the abstract change
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