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 $2n$-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 $D$ 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

AdS and Lifshitz Black Holes in Conformal and Einstein-Weyl Gravities

We study black hole solutions in extended gravities with higher-order curvature terms, including conformal and Einstein-Weyl gravities. In addition to the usual AdS vacuum, the theories admit Lifshitz and Schr\"odinger vacua. The AdS black hole in conformal gravity contains an additional parameter over and above the mass, which may be interpreted as a massive spin-2 hair. By considering the first law of thermodynamics, we find that it is necessary to introduce an associated additional intensive/extensive pair of thermodynamic quantities. We also obtain new Liftshitz black holes in conformal gravity and study their thermodynamics. We use a numerical approach to demonstrate that AdS black holes beyond the Schwarzschild-AdS solution exist in Einstein-Weyl gravity. We also demonstrate the existence of asymptotically Lifshitz black holes in Einstein-Weyl gravity. The Lifshitz black holes arise at the boundary of the parameter ranges for the AdS black holes. Outside the range, the solutions develop naked singularities. The asymptotically AdS and Lifshitz black holes provide an interesting phase transition, in the corresponding boundary field theory, from a relativistic Lorentzian system to a non-relativistic Lifshitz system.Comment: typos corrected, references adde

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 $p$-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 $2n$-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

Resolved Calabi-Yau Cones and Flows from L abc Superconformal Field Theories

We discuss D3-branes on cohomogeneity-three resolved Calabi-Yau cones over Labc spaces, for which a 2-cycle or 4-cycle has been blown up. In terms of the dual quiver gauge theory, this corresponds to motion along the non-mesonic, or baryonic, directions in the moduli space of vacua. In particular, a dimension-two and/or dimensionsix scalar operator gets a vacuum expectation value. These resolved cones support various harmonic (2, 1)-forms which reduce the ranks of some of the gauge groups either by a Seiberg duality cascade or by Higgsing. We also discuss higher-dimensional resolved Calabi-Yau cones. In particular, we obtain square-integrable (2, 2)-forms for eight-dimensional cohomogeneity-four Calabi-Yau metrics