12 research outputs found
Construction of Einstein-Sasaki metrics in D ≥ 7
We construct explicit Einstein-Kahler metrics in all even dimensions D=2n+4
\ge 6, in terms of a -dimensional Einstein-Kahler base metric. These are
cohomogeneity 2 metrics which have the new feature of including a NUT-type
parameter, in addition to mass and rotation parameters. Using a canonical
construction, these metrics all yield Einstein-Sasaki metrics in dimensions
D=2n+5 \ge 7. As is commonly the case in this type of construction, for
suitable choices of the free parameters the Einstein-Sasaki metrics can extend
smoothly onto complete and non-singular manifolds, even though the underlying
Einstein-Kahler metric has conical singularities. We discuss some explicit
examples in the case of seven-dimensional Einstein-Sasaki spaces. These new
spaces can provide supersymmetric backgrounds in M-theory, which play a role in
the AdS_4/CFT_3 correspondence.Comment: Latex, 18 pages, 2 figures, minor typos correcte
General Kerr-NUT-AdS Metrics in All Dimensions
The Kerr-AdS metric in dimension D has cohomogeneity [D/2]; the metric
components depend on the radial coordinate r and [D/2] latitude variables \mu_i
that are subject to the constraint \sum_i \mu_i^2=1. We find a coordinate
reparameterisation in which the \mu_i variables are replaced by [D/2]-1
unconstrained coordinates y_\alpha, and having the remarkable property that the
Kerr-AdS metric becomes diagonal in the coordinate differentials dy_\alpha. The
coordinates r and y_\alpha now appear in a very symmetrical way in the metric,
leading to an immediate generalisation in which we can introduce [D/2]-1 NUT
parameters. We find that (D-5)/2 are non-trivial in odd dimensions, whilst
(D-2)/2 are non-trivial in even dimensions. This gives the most general
Kerr-NUT-AdS metric in dimensions. We find that in all dimensions D\ge4
there exist discrete symmetries that involve inverting a rotation parameter
through the AdS radius. These symmetries imply that Kerr-NUT-AdS metrics with
over-rotating parameters are equivalent to under-rotating metrics. We also
consider the BPS limit of the Kerr-NUT-AdS metrics, and thereby obtain, in odd
dimensions and after Euclideanisation, new families of Einstein-Sasaki metrics.Comment: Latex, 24 pages, minor typos correcte
A Note on Einstein Sasaki Metrics in D \ge 7
In this paper, we obtain new non-singular Einstein-Sasaki spaces in
dimensions D\ge 7. The local construction involves taking a circle bundle over
a (D-1)-dimensional Einstein-Kahler metric that is itself constructed as a
complex line bundle over a product of Einstein-Kahler spaces. In general the
resulting Einstein-Sasaki spaces are singular, but if parameters in the local
solutions satisfy appropriate rationality conditions, the metrics extend
smoothly onto complete and non-singular compact manifolds.Comment: Latex, 13 page
AdS in Warped Spacetimes
We obtain a large class of AdS spacetimes warped with certain internal spaces
in eleven-dimensional and type IIA/IIB supergravities. The warp factors depend
only on the internal coordinates. These solutions arise as the near-horizon
geometries of more general semi-localised multi-intersections of -branes. We
achieve this by noting that any sphere (or AdS spacetime) of dimension greater
than 3 can be viewed as a foliation involving S^3 (or AdS_3). Then the S^3 (or
AdS_3) can be replaced by a three-dimensional lens space (or a BTZ black hole),
which arises naturally from the introduction of a NUT (or a pp-wave) to the
M-branes or the D3-brane. We then obtain multi-intersections by performing a
Kaluza-Klein reduction or Hopf T-duality transformation on the fibre coordinate
of the lens space (or the BTZ black hole). These geometries provide further
possible examples of the AdS/CFT correspondence and of consistent embeddings of
lower-dimensional gauged supergravities in D=11 or D=10.Comment: Latex file, 26 pages, reference adde
A New Construction of Einstein-Sasaki Metrics in D >= 7
We construct explicit Einstein-Kahler metrics in all even dimensions D=2n+4 \ge 6, in terms of a -dimensional Einstein-Kahler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, in addition to mass and rotation parameters. Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5 \ge 7. As is commonly the case in this type of construction, for suitable choices of the free parameters the Einstein-Sasaki metrics can extend smoothly onto complete and non-singular manifolds, even though the underlying Einstein-Kahler metric has conical singularities. We discuss some explicit examples in the case of seven-dimensional Einstein-Sasaki spaces. These new spaces can provide supersymmetric backgrounds in M-theory, which play a role in the AdS_7/CFT_6 correspondence