Supersymmetric Black Holes in AdS4 from Very Special Geometry

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 AdS4 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 Kahler manifold. When the resulting very special Kahler manifold is a homogeneous space, we find analytic solutions for static, supersymmetric AdS4 black holes with vanishing axions. The horizon geometries of our solutions are constant curvature Riemann surfaces of arbitrary genus.Comment: 22 page

d-Geometries Revisited

We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.Comment: 37 pages; some clarifications and 1 reference adde

Electric-Magnetic Duality in Supergravity and Extremal Black Hole Attractors

The low-energy limit of theories of gravity such as Superstring theory and $M$-theory is Supergravity, whose action contains the Einstein Hilbert term coupled to vector and scalar fields in the bosonic sector, and fermions of spin $1/2$ and spin-$3/2$ gravitinos in the fermionic sector, with a specific field content depending on the Supergravity theory under consideration. Following Gaillard-Zumino construction, we find that the most general duality group, whose action leaves the equations of motion invariant, is the symplectic Sp(2n, \bb R) group. When the effective duality group is a non compact subgroup of Sp(2n, \bb R), it is necessary to include scalar fields in the theory as coordinates of a manifold characterizing the Supergravity theory, describing a non linear $\sigma$-model. Black holes are states of the graviton spin 2 field in Supergravity spectrum. In the case of non thermal radiation these states are stable, as happens for electromagnetically charged black holes with zero temperature but finite entropy, a property called \textit{extremality}. Among these solutions, we consider static spherically symmetric systems in $d=4$ space-time dimensions, for which the dynamic is one dimensional and allows the determination of an effective potential depending on electromagnetic charges and scalar (moduli) fields, written in terms of dressed central (in case, also matter) charges, in \mc N=2 quadratic, \mc N=3,5 extended Supergravity. All of these theories have a scalar manifold \mc M_{scalar} which is a symmetric space and does not admit a $d=5$ uplift. Even if the black hole has a scalar hair, its entropy does depend only on asymptotical degrees of freedom, namely electric and magnetic charges determined by vector field strengths fluxes at spatial infinity. This behaviour is explained by the \textit{Attractor Mechanism}, since the vector multiplets scalars radial trajectories approach a fixed point in the moduli space as they reach the black hole horizon, loosing all memories of initial conditions. The fixed point is an equilibrium point for the system, and a critical one for the black hole effective potential. The supersymmetric (BPS) black hole in \mc N=2 quadratic Supergravity is the only solution in which all the scalars are stabilized and the moduli space is therefore empty. All the other studied solutions present flat directions for the scalar fields, but the attractor equations cancel the moduli dependence in the dynamical configuration at the black hole horizon. Specifically, the black hole entropy is given in terms of the invariant of the relevant $U$-duality group, which turns out to be a quadratic expression (in the case of \mc N=2 quadratic and \mc N=3 Supergravity), or a perfect square of a quadratic expression (in the case of \mc N=4 and \mc N=5 Supergravity) in terms of the eigenvalues of the central charge matrix. Due to the peculiarity of these theories it is possible to write an alternative expression for the Bekenstein-Hawking Entropy in terms of the \textit{effective horizon radius} $R_{H}$, whose expression is a function of scalar charges and the geometrical radius of the horizon, $r_{H}$. Non-BPS attractor flows of extremal black holes in $d=4$ can be described in the first order formalism, introducing a \textit{fake superpotential} \mc W such that \mc W(\phi_{\infty}, p,q)=~r_{H}(\phi_{\infty},p,q) that enters in the espression of the effective radius $R_{H}$; the latter turns out to be, for the above mentioned theories, a moduli independent quantity. As a counterexample, \mc N=4, $d=4$ Supergravity coupled to $1$ vector multiplet admits an uplift to \mc N=4 pure Supergravity in $d=5$ dimensions, but has a quartic invariant which cannot be written as a quadratic expression of the skew-eigenvalues of the central charge matrix, and the effective radius description does not hold. As a final discussion the dualities among bosonic sectors of extended Supergravities are presented to explicitely show that bosonic interacting theories do not have a unique supersymmetric extension

Holographic duals of 6d RG flows

A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer $N$, an ADE group $G$, and two nilpotent elements $\mu_\mathrm{L,R}$ 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 $G=\mathrm{SU}(k)$, where AdS$_7$ duals exist in IIA. We work with a seven-dimensional gauged supergravity, consisting of the gravity multiplet and two $\mathrm{SU}(k)$ 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.Comment: 33 pages, 2 figure

5d/4d U-dualities and N=8 black holes

We use the connection between the U-duality groups in d=5 and d=4 to derive properties of the N=8 black hole potential and its critical points (attractors). This approach allows to study and compare the supersymmetry features of different solutions.Comment: 23 pages, LaTeX; some notations cleared up; final version on Phys. Rev.

Islands and Light Gravitons in type IIB String Theory

We consider the setup of an evaporating black hole in AdS$_{4}$ coupled to an external bath, embedded in type IIB string theory. We study quantum extremal islands in these backgrounds, in relation to the existence of a massive graviton. Using explicit results of the microscopic embedding of AdS$_{4}$ massive gravity in string theory, we investigate whether it is possible to achieve backgrounds with extremal islands, in which the lowest lying graviton is only slightly massive. For certain regions of the microscopic parameters, the graviton mass can be computed explicitly, and we explain how it directly affects the existence and the properties of the islands. We also show that islands can in principle exist within the regime of validity of the massive gravity effective field theory. However we see via numerical computations that the existence of quantum extremal islands at zero temperature is highly constrained, also when the dilaton is allowed to vary, so that the mass of the graviton cannot be made arbitrarily light. At finite temperature, we also identify a critical parameter, above and below which islands still exist but exhibit a different behavior. Our work supports recent proposals that the unitary evolution of black holes in higher dimensions, and more precisely their Page curve, strongly relies on the presence of a massive graviton in the effective theory.Comment: 20 pages, 11 figures, 1 ancillary noteboo

d=4 Attractors, Effective Horizon Radius and Fake Supergravity

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\geq2 supergravities sharing the same full bosonic sector.Comment: 1+47 pages, 2 Tables. v2: Eqs. (2.3),(2.4) and Footnote 3 added; minor cosmetic changes; to appear in PR

Direct oral Xa inhibitors versus warfarin in patients with cancer and atrial fibrillation: a meta-analysis

Patients with cancer are at higher risk of atrial fibrillation, thromboembolic complications and bleeding events compared with the general population. The aim of the present meta-analysis was to compare the efficacy and safety of direct oral Xa inhibitor anticoagulants versus warfarin in patients with cancer and atrial fibrillation