No abstract

We present new results towards the construction of the most general black hole solutions in four-dimensional Fayet-Iliopoulos gauged supergravities. In these theories black holes can be asymptotically AdS and have arbitrary mass, angular momentum, electric and magnetic charges and NUT charge. Furthermore, a wide range of horizon topologies is allowed (compact and noncompact) and the complex scalar fields have a nontrivial radial and angular profile. We construct a large class of solutions in the simplest single scalar model with prepotential F = −iX 0 X 1 and discuss their thermodynamics. Moreover, various approaches and calculational tools for facing this problem with more general prepotentials are presented.

We consider extremal black hole attractors (both BPS and non-BPS) for N = 3 and N = 5 supergravity in d = 4 space-time dimensions.Attractors for matter-coupled N = 3 theory are similar to attractors in N = 2 supergravity minimally coupled to Abelian vector multiplets.On the other hand, N = 5 attractors are similar to attractors in N = 4 pure supergravity, and in such theories only 1 N -BPS non-degenerate solutions exist. All the above mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a d = 5 uplift.Finally we comment on the "duality" relations among the attractor solutions of N ≥ 2 supergravities sharing the same full bosonic sector. 8 Peculiarity of Pure N = 4 and N = 5 Supergravity 35 9 N 2 Supergravities with the same Bosonic Sector and "Dualities" 36 10 Conclusion 38 A Appendix I A Counterexample : N = 4 Matter-Coupled Supergravity 40 • N = 5 supergravity [74], with U -invariant quartic in BH charges.It is worth pointing out that N = 2 supergravity minimally coupled to one Abelian vector multiplet, corresponding to the (U (1)) 6 → (U (1)) 2 gauge truncation of N = 4 pure supergravity, is nothing but the so-called Maxwell-Einstein-axion-dilaton system, studied in [77,78] and recently discussed in [71] and in [63]. As stated above, the formula (1.3) indeed holds true (actually, with suitable changes, also in the non-extremal case).Furthermore, it is interesting to notice that all the above mentioned theories are all the N 2, d = 4 supergravities based on symmetric scalar manifolds which do not admit an uplift 1 to d = 5 space-time dimensions [81].The present paper is organized as follows.In Sect. 2 we briefly intoduce the fundamentals of the first order (fake supergravity) formalism for the non-degenerate attractor flows (both BPS and non-BPS) of extremal BHs in d = 4 space-time dimensions.Sect. 3 is thus devoted to a detailed study of N = 2, d = 4 supergravity minimally coupled to Abelian vector multiplets. In Subsect. 3.1 the related Attractor Equations are explicitly solved, for both the classes of non-degenerate critical points of V BH : the 1 2 -BPS one (Subsubsect. 3.1.1) and the non-BPS Z = 0 one, this latter with related moduli space (Subsubsect. 3.1.2). By exploiting the first order (fake supergravity) formalism, in Subsects. 3.2 and 3.3 the ADM (Arnowitt-Deser-Misner) mass M ADM [82], covariant scalar charges Σ i and (square) effective horizon radius R 2 H are explicitly computed respectively for 1 2 -BPS and non-BPS Z = 0 attractor flows, proving that the second line of Eq. (1.3) holds true. This latter result, already proved in [63], generalizes the findings of [77,78], also holding in the non-extremal case.Sect. 4 deals with N = 3, d = 4 supergravity coupled to matter (Abelian vector) multiplets. In Subsect. 4.1 the related Attractor Equations are explicitly solved, for both the classes of non-degenerate critical points of V BH : the 1 3 -BPS one (Subsubsect. 4.1.1) and the non-BPS Z AB = 0 one (Subsubsect. 4.1.2...

AdS 7 supersymmetric solutions in type IIA have been classified, and they are infinitely many. Moreover, every such solution has a non-supersymmetric sister. In this paper, we study the perturbative and non-perturbative stability of these non-supersymmetric solutions, focusing on cases without orientifolds. Perturbatively, we first look at the KK spectrum of spin-2 excitations. This does not exhibit instabilities, but it does show that there is no separation of scales for either the BPS and the non-BPS case, thus proving for supersymmetric AdS 7 a well-known recent conjecture. We then use 7d gauged supergravity and a brane polarization computation to access part of the spectrum of KK scalars. The result signals an instability for all non-supersymmetric solutions except those that have a single D8 on each side. We finally look at non-perturbative instabilities, and find that NS5 bubbles make these remaining solutions decay.

We examine a few simple extremal black hole configurations of N ¼ 8, d ¼ 4 supergravity. We first elucidate the relation between the BPS Reissner-Nördstrom black hole and the non-BPS Kaluza-Klein dyonic black hole. Their classical entropy, given by the Bekenstein-Hawking formula, can be reproduced via the attractor mechanism by suitable choices of symplectic frame. Then, we display the embedding of the axion-dilaton black hole into N ¼ 8 supergravity.

Supersymmetric black holes in AdS spacetime are inherently interesting for the AdS/CFT correspondence. Within a four dimensional gauged supergravity theory coupled to vector multiplets, the only analytic solutions for regular, supersymmetric, static black holes in AdS 4 are those in the STU-model due to Cacciatori and Klemm. We study a class of U (1)-gauged supergravity theories coupled to vector multiplets which have a cubic prepotential, the scalar manifold is then a very special Kähler manifold. When the resulting very special Kähler manifold is a homogeneous space, we find analytic solutions for static, supersymmetric AdS 4 black holes with vanishing axions. The horizon geometries of our solutions are constant curvature Riemann surfaces of arbitrary genus.

We consider theories of N = 2 supergravity with Fayet-Iliopoulos gauging and describe a procedure to obtain non-BPS extremal black hole solutions in asymptotically AdS 4 space, in a fully symplectic covariant framework.By considering both electric as well as magnetic gauging, we are able to find new extremal purely magnetic and dyonic solutions. We consistently impose the Dirac quantization condition as a constraint on the black hole and gravitinos charges. This additional requirement allows to parametrize the black hole entropy in terms of an integer and of the entropy of the corresponding black hole in the ungauged model.We also find the nonextremal generalization of the dyonic solution and we compute the product of the areas. For all the configurations with asymptotic supersymmetry we furthermore compute the mass.

A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer N , an ADE group G, and two nilpotent elements µ L,R in G. Nilpotent elements have a natural partial ordering, which has been conjectured to coincide with the hierarchy of renormalization-group flows among the SCFTs. In this paper we test this conjecture for G = SU(k), where AdS 7 duals exist in IIA. We work with a sevendimensional gauged supergravity, consisting of the gravity multiplet and two SU(k) non-Abelian vector multiplets. We show that this theory has many supersymmetric AdS 7 vacua, determined by two nilpotent elements, which are naturally interpreted as IIA AdS 7 solutions. The BPS equations for domain walls connecting two such vacua can be solved analytically, up to a Nahm equation with certain boundary conditions. The latter admit a solution connecting two vacua if and only if the corresponding nilpotent elements are related by the natural partial ordering, in agreement with the field theory conjecture.