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...upersymmetry when θ1 ̸= −θ2, whereas if θ1 = −θ2, ξ + preserves all supersymmetry and ξ− preserves ν = 1 2 . As shown in [49] and conjectured in [66], the quotient by ξ + is the near-horizon geometry =-=[67]-=- of the critically over-rotating black hole [68, 69]. 6.1.5. ξ = ξ (8) A + ξS. In this case, the Killing vector field is ξ ± = ∓e12 − e13 ± e24 + e34 + ϕ(e34 ± e12) + θ1R12 + θ2R34 , where θ1 ≥ |θ2| >...

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...precisely analogous to the D1/D5-system. That is far from the truth. The D1/D5 system is supersymmetric; indeed, it is the only case familiar to me where rotation is consistent with the BPS condition =-=[26, 27]-=-. Many of the remarkable properties discussed above follow from this fact. It is thus significant to emphasize that KaluzaKlein black holes are not supersymmetric. To see this, embed the simple Kaluza...

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... AdS3 × S 3 × S 3 is, generally, warped. The special case of solutions with space-time AdS3 × S 3 × S 3 × E2, where E2 is flat Euclidean, and the product is not warped, was analyzed in [27] (see also =-=[28, 29]-=-). Other types of solutions on various space-times with an AdS3 factor, and various degrees of supersymmetry, have been constructed in [30, 31, 32]. The Ansatz AdS3 ×S 3 ×S 3 ×Σ encompasses as special...

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...can be enhanced to eight Poincaré and four special conformal supersymmetries. Having constructed the explicit Killing spinors we can use them to study the superisometry algebra using the technique of =-=[7]-=-[8]. In particular, the Grassmann odd-odd part of this algebra is obtained by constructing Killing vectors as bi-linears in the Killing spinors. The odd-even part of the algebra is obtained by taking ...

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...f the type (1.2), but also suggest that fully back-reacted D7 brane solutions in AdS5 × S 5 should not exist. The correspondence may be further illustrated by the M-theory solutions of [11] (see also =-=[12, 13]-=-) and the M-theory solutions of [10], which both form families of solutions invariant under the exceptional Lie superalgebra H = D(2, 1; c; 0) ⊕ D(2, 1; c; 0). Here, c ̸= 0 is a free real parameter, a...

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...eometries that have closed time-like curves, like some of the Gödel universes described in [5], or black hole solutions. Let us take the solutions of IIA supergravity of the supertube family given by =-=[32, 31]-=- ds 2 = − U −1 V −1/2 (dt − A) 2 + U −1 V 1/2 dy 2 + V 1/2 B2 =U −1 (dt − A) ∧ dy − dt ∧ dy , C1 = − V −1 (dt − A) + dt , 8∑ i=1 (dx i ) 2 (2.8) C3 = − U −1 dt ∧ dy ∧ A, e Φ =U −1/2 V 3/4 . – 4 –Here...

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...x i ), the Killing spinors are given by ǫ = θ + + (1 + Jijx i γ j )θ − where θ ± are constant spinors satisfying γ 0 θ ± = ±θ ± . (3.31) We can determine the symmetry superalgebra using the method of =-=[34]-=- (see also [35, 36, 37]). This is a Lie-superalgebra whose even subspace B is spanned by the above Killing-vectors and the odd subspace F by the Killing spinors. The bilinear map B × B → B is the Lie-...

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...eometries that have closed time-like curves, like some of the Gödel universes described in [5], or black hole solutions. Let us take the solutions of IIA supergravity of the supertube family given by =-=[32, 31]-=- ds 2 = − U −1 V −1/2 (dt − A) 2 + U −1 V 1/2 dy 2 + V 1/2 B2 =U −1 (dt − A) ∧ dy − dt ∧ dy , C1 = − V −1 (dt − A) + dt , 8∑ i=1 (dx i ) 2 (2.8) C3 = − U −1 dt ∧ dy ∧ A, e Φ =U −1/2 V 3/4 . – 4 –Here...