We construct the non-linear Kaluza-Klein ansätze describing the embeddings of the U (1) 3 , U (1) 4 and U (1) 2 truncations of D = 5, D = 4 and D = 7 gauged supergravities into the type IIB string and M-theory. These enable one to oxidise any associated lower dimensional solutions to D = 10 or D = 11. In particular, we use these general ansätze to embed the charged AdS 5 , AdS 4 and AdS 7 black hole solutions in ten and eleven dimensions.The charges for the black holes with toroidal horizons may be interpreted as the angular momenta of D3-branes, M2-branes and M5-branes spinning in the transverse dimensions, in their near-horizon decoupling limits. The horizons of the black holes coincide with the worldvolumes of the branes. The Kaluza-Klein ansätze also allow the black holes with spherical or hyperbolic horizons to be reinterpreted in D = 10 or D = 11. IntroductionAnti-de Sitter black hole solutions of gauged extended supergravities [1] are currently attracting a good deal of attention [2,3,4,5,6,7,8,9,10,11,12] due, in large part, to the correspondence between anti-de Sitter space and conformal field theories on its boundary [13,14,15,16]. These gauged extended supergravities can arise as the massless modes of various Kaluza-Klein compactifications of both D = 11 and D = 10 supergravities. The three examples studied in the paper will be gauged D = 4, N = 8 SO(8) supergravity [17, 18] arising from D = 11 supergravity on S 7 [19, 20] whose black hole solutions are discussed in [7]; gauged D = 5, N = 8 SO(6) supergravity [21, 22] arising from Type IIB supergravity on S 5 [23, 24, 25] whose black hole solutions are discussed in [2, 6]; and gauged D = 7, N = 4 SO(5) supergravity [21, 26] arising from D = 11 supergravity on S 4 [27]whose black hole solutions are given in section 4.2 and in [9,28]. 1 In the absence of the black holes, these three AdS compactifications are singled out as arising from the near-horizon geometry of the extremal non-rotating M2, D3 and M5 branes [29,30,31,32]. One of our goals will be to embed these known lower-dimensional black hole solutions into ten or eleven dimensions, thus allowing a higher dimensional interpretation in terms of rotating M2, D3 and M5-branes.Since these gauged supergravity theories may be obtained by consistently truncating the massive modes of the full Kaluza-Klein theories, it follows that all solutions of the lower-dimensional theories will also be solutions of the higher-dimensional ones [33,34]. In principle, therefore, once we know the Kaluza-Klein ansatz for the massless sector, it ought to be straightforward to read off the higher dimensional solutions. It practice, however, this is a formidable task. The correct massless ansatz for the S 7 compactification took many years to finalize [35,36], and is still highly implicit, while for the S 5 and S 4 compactifications, the complete massless ansätze are still unknown. For our present purposes, it suffices to consider truncations of the gauged supergravities to include only gauge fields in the Cartan subalgebras ...

We analyse the global (rigid) symmetries that are realised on the bosonic fields of the various supergravity actions obtained from eleven-dimensional supergravity by toroidal compactification followed by the dualisation of some subset of fields. In particular, we show how the global symmetries of the action can be affected by the choice of this subset. This phenomenon occurs even with the global symmetries of the equations of motion. A striking regularity is exhibited by the series of theories obtained respectively without any dualisation, with the dualisation of only the Ramond-Ramond fields of the type IIA theory, with full dualisation to lowest degree forms, and finally for certain inverse dualisations (increasing the degrees of some forms) to give the type IIB series. These theories may be called the GL A , D, E and GL B series respectively. It turns out that the scalar Lagrangians of the E series are sigma models on the symmetric spaces K(E 11−D )\E 11−D (where K(G) is the maximal compact subgroup of G) and the other three series lead to models on homogeneous spaces K(G)\G⋉IR s . These can be understood from the E series in terms of the deletion of positive roots associated with the dualised scalars, which implies a group contraction. We also propose a constrained Lagrangian version of the even dimensional theories exhibiting the full duality symmetry and begin a systematic analysis of abelian duality subalgebras.implemented only on the field strengths (necessarily in the equations of motion), then all the members of the multiplet must appear in the field equations and Bianchi identities only through their field strengths. If the result of dualisations is to make it that neither of these conditions is satisfied, then the original global symmetry prior to the dualisations will be broken.The fact that the global symmetry can depend on the choice of dualisation [12], and the fact that not all dualisations are possible, are both consequences of the occurrence of nonlinear terms in the D-dimensional Lagrangian. These terms have two origins, namely the F (4) ∧ F (4) ∧ A (3) term in the original eleven-dimensional Lagrangian, and the non-linearity of the eleven-dimensional Einstein-Hilbert action. The latter implies that modifications to the field strengths in lower dimensions will arise in the Kaluza-Klein reduction process. These are sometimes called "Chern-Simons modifications," but the term is really a misnomer since they actually come from the separation between the gauge transformations originating from diffeomorphisms along the compactified directions and the other gauge symmetries. In this paper they will be called Kaluza-Klein modifications. In order to investigate these issues in more detail it is convenient to divide the discussion into two parts, namely for the subsector comprising the scalar fields, and then the remaining sectors involving the higher-degree field strengths.In any dimension D ≥ 6, the scalar sector of the D-dimensional theory that is obtained by dimensional reduction from D = 11 is unam...

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We give the general Kerr-de Sitter metric in arbitrary spacetime dimension D ≥ 4, with the maximal number [(D − 1)/2] of independent rotation parameters. We obtain the metric in Kerr-Schild form, where it is written as the sum of a de Sitter metric plus the square of a null-geodesic vector, and in generalised Boyer-Lindquist coordinates. The Kerr-Schild form is simpler for verifying that the Einstein equations are satisfied, and we have explicitly checked our results for all dimensions D ≤ 11. We discuss the global structure of the metrics, and obtain formulae for the surface gravities and areas of the event horizons.We also obtain the Euclidean-signature solutions, and we construct complete non-singular compact Einstein spaces on associated S D−2 bundles over S 2 , infinitely many for each odd D ≥ 5.

Seven-manifolds of G 2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six-manifolds. We find first-order equations for a new family of G 2 metrics D 7 , with S 3 × S 3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B 7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D 7 metrics' non-trivial parameter characterises the squashing of an S 3 bolt, which limits to S 2 at weak coupling. In general the D 7 metrics are asymptotically locally conical, with a nowhere-singular circle action.