Supersymmetric Black Hole Solutions Research Articles

Supersymmetric charge constraints on AdS black holes from free fields

Supersymmetric AdS black hole solutions exist only when their angular momenta and charges satisfy a certain constraint that depends on the dimension. We show that these nonlinear relations on the conserved charges agree with a computation in the dual supersymmetric CFT in its free limit, with interactions entering only through a uniform rescaling of all charges. Our computations apply to the highly non-trivial charge constraints for AdS4, AdS5 and AdS7 black holes, and generalize an earlier one for the analogous constraint in AdS3. Our results suggest a microscopic understanding of AdS black holes beyond the scope of supersymmetric indices.

All separable supersymmetric AdS5 black holes

We consider the classification of supersymmetric black hole solutions to five-dimensional STU gauged supergravity that admit torus symmetry. This reduces to a problem in toric Kähler geometry on the base space. We introduce the class of separable toric Kähler surfaces that unify product-toric, Calabi-toric and orthotoric Kähler surfaces, together with an associated class of separable 2-forms. We prove that any supersymmetric toric solution that is timelike, with a separable Kähler base space and Maxwell fields, outside a horizon with a compact (locally) spherical cross-section, must be locally isometric to the known black hole or its near-horizon geometry. An essential part of the proof is a near-horizon analysis which shows that the only possible separable Kähler base space is Calabi-toric. In particular, this also implies that our previous black hole uniqueness theorem for minimal gauged supergravity applies to the larger class of separable Kähler base spaces.

Black hole entropy from quantum mechanics

We provide evidence for a holographic duality between superconformal quantum mechanics on the moduli space of Yang-Mills instantons and M-theory in certain asymptotically AdS7 × S4 backgrounds with a plane-wave boundary metric. We show that the gravitational background admits a supersymmetric black hole solution whose entropy is precisely reproduced by the superconformal index of the dual quantum mechanics.

Supersymmetric Black Holes with a Single Axial Symmetry in Five Dimensions

We present a classification of asymptotically flat, supersymmetric black hole and soliton solutions of five-dimensional minimal supergravity that admit a single axial symmetry which ‘commutes’ with the supersymmetry. This includes the first examples of five-dimensional black hole solutions with exactly one axial Killing field that are smooth on and outside the horizon. The solutions have similar properties to the previously studied class with biaxial symmetry, in particular, they have a Gibbons–Hawking base and the harmonic functions must be of multi-centred type with the centres corresponding to the connected components of the horizon or fixed points of the axial symmetry. We find a large moduli space of black hole and soliton spacetimes with non-contractible 2-cycles and the horizon topologies are S^3, S^1times S^2 and lens spaces L(p, 1).

On the uniqueness of supersymmetric AdS(5) black holes with toric symmetry

We consider the classification of supersymmetric AdS5 black hole solutions to minimal gauged supergravity that admit a torus symmetry. This problem reduces to finding a class of toric Kähler metrics on the base space, which in symplectic coordinates are determined by a symplectic potential. We derive the general form of the symplectic potential near any component of the horizon or axis of symmetry, which determines its singular part for any black hole solution in this class, including possible new solutions such as black lenses and multi-black holes. We find that the most general known black hole solution in this context, found by Chong, Cvetic, Lü and Pope (CCLP), is described by a remarkably simple symplectic potential. We prove that any supersymmetric and toric solution that is timelike outside a smooth horizon, with a Kähler base metric of Calabi type, must be the CCLP black hole solution or its near-horizon geometry.

A note on co-dimension 2 defects in N = 4,d = 7 gauged supergravity

In this note we present a solution of N=4,d=7 gauged supergravity which is holographically dual to a co-dimension two defect living in a six dimensional SCFT. The solution is obtained by double analytic continuation of a two charge supersymmetric black hole solution. The condition that no conical deficits are present in the bulk and on the boundary is satisfied by a one parameter family of solutions for which some holographic observables are computed.

The large-N limit of the 4d mathcal{N} = 1 superconformal index

We systematically analyze the large-N limit of the superconformal index of mathcal{N} = 1 superconformal theories having a quiver description. The index of these theories is known in terms of unitary matrix integrals, which we calculate using the recently-developed technique of elliptic extension. This technique allows us to easily evaluate the integral as a sum over saddle points of an effective action in the limit where the rank of the gauge group is infinite. For a generic quiver theory under consideration, we find a special family of saddles whose effective action takes a universal form controlled by the anomaly coefficients of the theory. This family includes the known supersymmetric black hole solution in the holographically dual AdS5 theories. We then analyze the index refined by turning on flavor chemical potentials. We show that, for a certain range of chemical potentials, the effective action again takes a universal cubic form that is controlled by the anomaly coefficients of the theory. Finally, we present a large class of solutions to the saddle-point equations which are labelled by group homomorphisms of finite abelian groups of order N into the torus.

Holographic renormalization group flows in two-dimensional gravity and AdS black holes

We look into the AdS black holes from two-dimensional gravity perspective. In this work, we extend the previous results of holographic renormalization group flows to dimensions two. By introducing a superpotential, we derive the flow equations in two-dimensional dilaton gravity. We also find a quantity which monotonically decreases along flows and give some comments on holographic c-theorem. As examples, we show that recently studied supersymmetric AdS black hole solutions generically dimensionally reduce to two-dimensional dilaton gravity, and obtain the flow equations for black hole solutions.

Constructing black hole solutions in supergravity theories

We perform a detailed analysis of black hole solutions in supergravity models. After a general introduction on black holes in general relativity and supersymmetric theories, we provide a detailed description of ungauged extended supergravities and their dualities. Therefore, we analyze the general form of black hole configurations for these models, their near-horizon behavior and characteristic of the solution. An explicit construction of a black hole solution with its physical implications is given for the STU-model. The second part of this review is dedicated to gauged supergravity theories. We describe a step-by-step gauging procedure involving the embedding tensor formalism to be used to obtain a gauged model starting from an ungauged one. Finally, we analyze general black hole solutions in gauged models, providing an explicit example for the [Formula: see text], [Formula: see text] case. A brief review on special geometry is also provided, with explicit results and relations for supersymmetric black hole solutions.

Non-Abelian rotating black holes in 4- and 5-dimensional gauged supergravity

We present new supersymmetric black-hole solutions of the 4- and 5-dimensional gauged supergravity theories that one obtains by dimensional reduction on T5 and T6 of Heterotic supergravity with a triplet of Yang-Mills fields. The new ingredient of our solutions is the presence of dyonic non-Abelian fields which allows us to obtain a generalization of the BMPV black hole with two independent angular momenta and the first example of a supersymmetric, rotating, asymptotically-flat black hole with a regular horizon in 4 dimensions.

General supersymmetric hbox {AdS}_5 black holes with squashed boundary

We present a new family of asymptotically locally hbox {AdS}_5 squashed supersymmetric black hole solutions of Fayet–Iliopoulos gauged {{{mathcal {N}}}}=2, D=5 supergravity with two vector multiplets that have a natural uplift to type IIB supergravity. Our new family of black holes is characterized by three parameters, of which two control the horizon geometry while the latter regulates the squashing at the boundary. We evaluate the main physical properties of the family of solutions using holographic renormalization and find that the entropy is independent on the squashing and it is reproduced by using the angular momentum and the Page charges. In previously known solutions Page and holographic charges are equal, due to the vanishing of the Chern–Simons term that here, instead, is relevant. This result suggests that for asymptotically locally hbox {AdS}_5 solutions we should refer to the Page charges to describe the thermodynamics of the system.

Supersymmetric near-horizon geometry and Einstein-Cartan-Weyl spaces

We show that the horizon geometry for supersymmetric black hole solutions of minimal five-dimensional gauged supergravity is that of a particular Einstein-Cartan-Weyl (ECW) structure in three dimensions, involving the trace and traceless part of both torsion and nonmetricity, and obeying some precise constraints. In the limit of zero cosmological constant, the set of nonlinear partial differential equations characterizing this ECW structure reduces correctly to that of a hyper-CR Einstein-Weyl structure in the Gauduchon gauge, which was shown by Dunajski, Gutowski and Sabra to be the horizon geometry in the ungauged BPS case.

Supersymmetric black hole non-uniqueness in five dimensions

We present a systematic study of the moduli space of asymptotically flat, supersymmetric and biaxisymmetric black hole solutions to five-dimensional minimal supergravity. Previously, it has been shown that such solutions must be multi-centred solutions with a Gibbons-Hawking base. In this paper we perform a full analysis of three-centred solutions with a single black hole, for which there are seven regular black hole solutions. We find that four of these can have the same conserved charges as the BMPV black hole. These consist of a black lens with L(3, 1) horizon topology and three distinct families of spherical black holes with nontrivial topology outside the horizon. The former provides the first example of a nonspherical black hole with the same conserved charges as the BMPV black hole. Moreover, of these four solutions, three can have a greater entropy than the BMPV black hole near the BMPV upper spin bound. One of these is a previously known spherical black hole with nontrivial topology and the other two are new examples of a spherical black hole with nontrivial topology and an L(3, 1) black lens.

Moduli Space of Supersymmetric Solitons and Black Holes in Five Dimensions

We determine all asymptotically flat, supersymmetric and biaxisymmetric soliton and black hole solutions to five-dimensional minimal supergravity. In particular, we show that the solution must be a multi-centred solution with a Gibbons–Hawking base. The proof involves combining local constraints from supersymmetry with global constraints for stationary and biaxisymmetric spacetimes. This reveals that the horizon topology must be one of S3, {{S}^{1}times {S}^{2}} or a lens space L(p, 1), thereby providing a refinement of the allowed horizon topologies.We construct the general smooth solution for each possible rod structure. We find a large moduli space of black hole spacetimes with noncontractible 2-cycles for each of the allowed horizon topologies. In the absence of a black hole, we obtain a classification of the known ‘bubbling’ soliton spacetimes.

Extremal higher spin black holes

The gauge sector of three-dimensional higher spin gravities can be formulated as a Chern-Simons theory. In this context, a higher spin black hole corresponds to a flat connection with suitable holonomy (smoothness) conditions which are consistent with the properties of a generalized thermal ensemble. Building on these ideas, we discuss a definition of black hole extremality which is appropriate to the topological character of 3d higher spin theories. Our definition can be phrased in terms of the Jordan class of the holonomy around a non-contractible (angular) cycle, and we show that it is compatible with the zero-temperature limit of smooth black hole solutions. While this notion of extremality does not require supersymmetry, we exemplify its consequences in the context of sl(3|2) + sl(3|2) Chern-Simons theory and show that, as usual, not all extremal solutions preserve supersymmetries. Remarkably, we find in addition that the higher spin setup allows for non-extremal supersymmetric black hole solutions. Furthermore, we discuss our results from the perspective of the holographic duality between sl(3|2) + sl(3|2) Chern-Simons theory and two-dimensional CFTs with W_{(3|2)} symmetry, the simplest higher spin extension of the N=2 super-Virasoro algebra. In particular, we compute W_{(3|2)} BPS bounds at the full quantum level, and relate their semiclassical limit to extremal black hole or conical defect solutions in the 3d bulk. Along the way, we discuss the role of the spectral flow automorphism and provide a conjecture for the form of the semiclassical BPS bounds in general N=2 two-dimensional CFTs with extended symmetry algebras.

Supersymmetric backgrounds and black holes in N = 1 , 1 $$ \mathcal{N}=\left(1,\;1\right) $$ cosmological new massive supergravity

Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the ${\cal N}=(1,1)$ Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the ${\cal N}=1$ model but we find new solutions with a time-like Killing vector that are absent in the ${\cal N}=1$ case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an $AdS_3$ background. Furthermore, we show that under certain assumptions there is no supersymmetric Lifshitz black hole solution.

Supersymmetric black holes and attractors in gauged supergravity with hypermultiplets

We consider four-dimensional N = 2 supergravity coupled to vector- and hypermultiplets, where abelian isometries of the quaternionic Kahler hypermultiplet scalar manifold are gauged. Using the recipe given by Meessen and Ortin in arXiv:1204.0493, we analytically construct a supersymmetric black hole solution for the case of just one vector multiplet with prepotential $$ \mathrm{\mathcal{F}}=-i{\chi}^0{\chi}^1 $$ , and the universal hypermultiplet. This solution has a running dilaton, and it interpolates between AdS2 × H2 at the horizon and a hyperscaling-violating type geometry at infinity, conformal to AdS2 × H2. It carries two magnetic charges that are completely fixed in terms of the parameters that appear in the Killing vector used for the gauging. In the second part of the paper, we extend the work of Bellucci et al. on black hole attractors in gauged supergravity to the case where also hypermultiplets are present. The attractors are shown to be governed by an effective potential V eff, which is extremized on the horizon by all the scalar fields of the theory. Moreover, the entropy is given by the critical value of V eff. In the limit of vanishing scalar potential, V eff reduces (up to a prefactor) to the usual black hole potential.

Super-Rényi entropy & Wilson loops for $$ \mathcal{N}=4 $$ SYM and their gravity duals

Abstract We compute the supersymmetric Rényi entropies across a spherical entanglement surface in $$ \mathcal{N}=4 $$ N = 4 SU(N) SYM theory using localization on the four-dimensional ellipsoid. We extract the leading result at large N and λ and match its universal part to a gravity calculation involving a hyperbolically sliced supersymmetric black hole solution of $$ \mathcal{N}={4}^{+} $$ N = 4 + SU(2) × U(1) gauged supergravity in five dimensions. We repeat the analysis in the presence of a Wilson loop insertion and find again a perfect match with the dual string theory. Understanding the Wilson loop operator requires knowledge of the full ten-dimensional IIB supergravity solution which we elaborate upon.

Black hole non-uniqueness via spacetime topology in five dimensions

The domain of outer communication of five-dimensional asymptotically flat stationary spacetimes may possess non-trivial 2-cycles. We discuss how this may lead to a gross violation of black hole uniqueness, beyond the existence of black rings, even for solutions with two commuting rotational symmetries. We illustrate this with a simple example in minimal supergravity; a four parameter family of supersymmetric black hole solutions, with spherical horizon topology and a 2-cycle in the exterior. We show there are black holes in this family with identical conserved changes to the BMPV black hole, thereby demonstrating black hole non-uniqueness in this context. We find a decoupling limit of this family of black holes that yields spacetimes asymptotic to the near-horizon geometry of a BMPV black hole which contain a black hole and an exterior 2-cycle.

The violation of the no-hair conjecture in four-dimensional ungauged supergravity

By choosing a particular, string-theory-inspired, special Kähler manifold, we are able to find an four-dimensional ungauged supergravity model that contains supersymmetric black hole solutions that violate the folk uniqueness theorems that are expected to hold in ungauged supergravity. The black hole solutions are regular in the sense that they have a positive mass and a unique physical singularity hidden by an event horizon. In contradistinction to most examples already known in the literature, we find our solutions in a theory without scalar potential, gaugings, or higher-order curvature terms.