Using the harmonic superspace method and the duality between real and complex representations of hypermultiplets, we compute the explicit scalar field expression of the quaternionic metric $G_{mn}$ of the moduli space SO(1,1)x[SO(4,k)/(SO(4)xSO(k))] of 6D N=2 supergravity with generic k Maxwell supermultiplets. The obtained metric includes the particular case k=20 associated with 10D type IIA superstring on K3. Uplifting to 7D N=2 supergravity is described and aspects of 6D/7D black attractor effective potentials are studied.
Employing uplift formulae, we uplift supersymmetric $AdS_6$ black holes from $F(4)$ gauged supergravity to massive type IIA and type IIB supergravity. In massive type IIA supergravity, we obtain supersymmetric $AdS_6$ black holes asymptotic to the Brandhuber-Oz solution. In type IIB supergravity, we obtain supersymmetric $AdS_6$ black holes asymptotic to the non-Abelian T-dual of the Brandhuber-Oz solution. For the uplifted black hole solutions, we calculate the holographic entanglement entropy. In massive type IIA supergravity, it precisely matches the Bekenstein-Hawking entropy of the black …
We present stationary, nonextremal three charge rotating black hole solutions in the five-dimensional U(1)^3 ungauged supergravity. At infinity, our solutions behave as a four-dimensional flat spacetime with a compact extra-dimension and hence describe spherical black holes with Kaluza-Klein asymptotics.
We have learnt that the Bekenstein-Hawking entropy of supersymmetric black holes in five-dimensional minimal supergravity can be reproduced from microstate counting via the AdS/CFT and Kerr/CFT correspondence. In this note, we demostrate the coincidence of both formalisms for extremal and near-extremal black holes in five-dimensional minimal supergravity. Connection to AdS_2 gravity is also mentioned.
Magnetic and Dyonic solutions are constructed for the theory of abelian gauged N=2 gauged four dimensional supergravity coupled to vector multiplets. The solutions found preserve 1/4 of the supersymmetry.
We present new supersymmetric black-hole solutions of the 4- and 5-dimensional gauged supergravity theories that one obtains by dimensional reduction on $T^{5}$ and $T^{6}$ 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.
We present the main features of the physics of extremal black holes embedded in supersymmetric theories of gravitation, with a detailed analysis of the attractor mechanism for BPS and non-BPS black-hole solutions in four dimensions.
We retrieve the non-BPS extremal black hole superpotential of N=8, d=4 supergravity by using the Maurer-Cartan equations of the symmetric space E_7(7)/SU(8). This superpotential was recently obtained with different 3- and 4-dimensional techniques. The present derivation is independent on the reduction to d=3.
In this note, we propose the free energy of general \emph{non-supersymmetric} black hole attractors arising in type IIA(B) superstrings on 3-fold Calabi-Yau, in the supergravity limit. This, by definition, differs from its counterpart BPS free energy by a factor of $4 $. Correspondingly, a mixed ensemble for these black holes is proposed.
We give an elementary introduction to black holes in supergravity and string theory. The focus is on BPS solutions in four- and higher-dimensional supergravity and string theory. Basic ideas and techniques are explained in detail, including exercises with solutions.
We demonstrate a solution generating technique, modulo some constraints, for a large class of smooth supergravity solutions with the same asymptotic charges as a five dimensional 3-charge BPS black hole or black ring, dual to a D1/D5/P system. These solutions are characterized by a harmonic function with both positive and negative poles, which induces a geometric transition whereby singular sources have disappeared and all of the net charge at infinity is sourced by fluxes through two-cycles joining the poles of the harmonic function.
We review some results on the connection among supergravity central charges, BPS states and Bekenstein-Hawking entropy. In particular, N=2 supergravity in four dimensions is studied in detail. For higher N supergravities we just give an account of the general theory specializing the discussion to the N=8 case when one half of supersymmetry is preserved. We stress the fact that for extremal supergravity black holes the entropy formula is topological, that is the entropy turns out to be a moduli independent quantity and can be written in terms of invariants of the duality group of the supergravi…
This book chapter presents a brief introduction to black holes and branes in supergravity, focussing on 11-dimensional supergravity and type II supergravities in 10-dimension. The chapter is aimed at graduate students who have completed a standard course in general relativity. It is an ammended and slightly updated version of arXiv:gr-qc/9908045. In addition to describing specific solutions, brief discussions of p-form gauge fields, Kaluza-Klein reduction, (local) supersymmetry, T- and S-dualities in supergravity, and string perturbation theory are included to provide context.
With the general aim to classify BPS solutions in N=2, D=5 supergravity with hypermultiplets and vector multiplets, here we consider a family of static spacetime metrics containing black hole-like solutions, with generic hypermultiplets coupled to radially symmetric electrostatic vector multiplets. We derive the general conditions which the fields must satisfy and determine the form of the fixed point solutions.
The assumptions behind the recently conjectured relation between gauge theory and supergravity are elaborated on. It is pointed out that the scaling limit that preserves supergravity solutions, gives the entire DBI action on the gauge theory side, but in the low energy limit the relation between the conformal field theory and Anti-de Sitter supergravity emerges. We also argue that recent work on these issues may help in understanding the physics of five (four) dimensional black hole with three (four) charges in the so-called dilute gas region.
We study stationary black brane solutions in the context of N = 2, U(1) gauged supergravity in five dimensions. Using the formalism of first-order flow equations, we construct examples of extremal black brane solutions that include Nernst branes, i.e. extremal black brane solutions with vanishing entropy density, as well as black branes with cylindrical horizon topology, whose entropy density can be computed from a Cardy formula of the dual CFT.
Electrically charged solutions breaking half of the supersymmetry in Anti-De Sitter four dimensional N=2 supergravity coupled to vector supermultiplets are constructed. These static black holes live in an asymptotic $AdS_4$ space-time. The Killing spinor, i. e., the spinor for supersymmetry variation is explicitly constructed for these solutions.
Supersymmetric terms in the effective action of N=2 supergravity in four dimensions are generically classified into chiral-superspace integrals and full-superspace integrals. For a theory of N=2 vector multiplets coupled to supergravity, a special class of couplings is given by chiral-superspace integrals that are governed by a holomorphic prepotential function. The quantum entropy of BPS black holes in such theories depends on the prepotential according to a known integral formula. We show, using techniques of localization, that a large class of full-superspace integrals in the effective acti…
Motivated by the new higher D-supergravity solutions on intersecting attractors obtained by Ferrara et al. in [Phys.Rev.D79:065031-2009], we focus in this paper on 8D maximal supergravity with moduli space [SL(3,R)/SO(3)]x[SL(2,R)/SO(2)] and study explicitly the attractor mechanism for various configurations of extremal black p- branes (anti-branes) with the typical near horizon geometries AdS_{p+2}xS^{m}xT^{6-p-m} and p=0,1,2,3,4; 2<=m<=6. Interpretations in terms of wrapped M2 and M5 branes of the 11D M-theory on 3-torus are also given. Keywords: 8D supergravity, black p-branes, attractor me…
We study $N=2$ gauged supergravity with $U(1)$ gauge group coupled to $n_v$ vector multiplets and find quite general analytic solutions for quarter-BPS black holes with mass, NUT and dyonic Maxwell charges. The solutions we find have running scalar fields and flow in the IR region to a horizon geometry of the form AdS$_2\times Σ_g$.
In this talk, I will summarize recent developments in 5-dimensional supergravity. Apart from black ring solutions, we will discuss the way of obtaining regular (bubbling) solutions with the same charges as black holes. We outline the procedure for the solution in five and four dimensions. Finally we explore the close relationship between 4- and 5-dimensional supersymmetric stationary solutions.
We study the doubly charged Callan-Giddings-Harvey-Strominger (CGHS) model, which has black hole solutions that were found to be U-dual to the D1-D5-KK black holes of the IIB supergravity. We derive the action of the model via a spontaneous compactification on S^3 of the IIB supergravity on S^1*T^4 and obtain the general static solutions including black holes corresponding to certain non-asymptotically flat black holes in the IIB supergravity. Thermodynamics of them is established by computing the entropy, temperature, chemical potentials, and mass in the two-dimensional setup, and the first l…
We obtain the general solution for non-extremal 3-charge dilatonic rotating black holes in the U(1)^3 gauged five-dimensional N=2 supergravity coupled to two vector multiplets, in the case where the two rotation parameters are set equal. These solutions encompass all the previously-known extremal solutions, and, by setting the three charges equal, the recently-obtained non-extremal solutions of N=2 gauged five-dimensional pure supergravity.
We discuss some of the basic features of extremal black holes in four-dimensional extended supergravities. Firstly, all regular solutions display an attractor behavior for the scalar field evolution towards the black hole horizon. Secondly, they can be obtained by solving first order flow equations even when they are not supersymmetric, provided one identifies a suitable superpotential W which also gives the black hole entropy at the horizon and its ADM mass at spatial infinity. We focus on N=8 supergravity and we review the basic role played by U-duality of the underlying supergravity in dete…
We construct black ring solutions in five-dimensional $U(1)^3$ supergravity which carry three dipole charges, three electric charges and one angular momentum parameter. These solutions are written in a form that is sufficiently compact that their global and thermodynamic properties can be studied explicitly. In particular, we find that the Smarr formula is obeyed regardless of whether or not conical singularities are present, whereas the first law of thermodynamics holds only in the absence of conical singularities. We also present black ring solutions with three background magnetic fields.
We study the embedding of extreme (multi-) dilaton black hole solutions for the values of the parameter $a=\sqrt{3},1,1/\sqrt{3},0$ in $N=4$ and $N=8$ four-dimensional supergravity. For each black hole solution we find different embeddings in $N=4$ supergravity which have different numbers of unbroken supersymmetries. When embedded in $N=8$ supergravity, all different embeddings of the same solution have the same number of unbroken supersymmetries. Thus, there is a relation between the value of the parameter $a$ and the number of unbroken supersymmetries in $N=8$ supergravity, but not in $N=4$…
In this paper we consider the four dimensional N=2 supergravity theory arising from the compactification of type IIA string theory on a Calabi-Yau manifold. We analyse the supersymmetric flow equations for static, spherically symmetric, single-centered black holes. These flow equations are solved by a set of algebraic equations involving the holomorphic sections and harmonic functions. We examine black hole configurations with D0-D4-D6 charge for which the most general solution of these algebraic equations are considered. Though the black hole solution is unique for a given value of the charge…
We compute the logarithmic correction to black hole entropy about exponentially suppressed saddle points of the Quantum Entropy Function corresponding to Z(N) orbifolds of the near horizon geometry of the extremal black hole under study. By carefully accounting for zero mode contributions we show that the logarithmic contributions for quarter--BPS black holes in N=4 supergravity and one--eighth BPS black holes in N=8 supergravity perfectly match with the prediction from the microstate counting. We also find that the logarithmic contribution for half--BPS black holes in N = 2 supergravity depen…
In the present paper we show that for a low frequency limit the wave equation of massless scalar field in the background of non-extremal charged rotating black holes in five-dimensional minimal gauged and ungauged supergravity can be written as the Casimir of an $SL(2,R)$ symmetry, our result show that the entropy of the black hole is reproduced by the Cardy formula, also the absorption cross section is in consistence with the finite temperature absorption cross section for a 2D CFT.
We construct new non-extremal rotating black hole solutions in SO(6) gauged five-dimensional supergravity. Our solutions are the first such examples in which the two rotation parameters are independently specifiable, rather than being set equal. The black holes carry charges for all three of the gauge fields in the U(1)^3 subgroup of SO(6), albeit with only one independent charge parameter. We discuss the BPS limits, showing in particular that these include the first examples of regular supersymmetric black holes with independent angular momenta in gauged supergravity. We also find non-singula…
We consider the stationary solutions of N=4 supergravity coupled to n vector multiplets that define linear superpositions of non-interacting extremal black holes. The most general solutions of this type are derived from the graded decompositions of so(8,2+n) associated to its nilpotent orbits. We illustrate the formalism by giving explicitly asymptotically Minkowski non-BPS solutions of the most exotic class depending on 6+n harmonic functions.
We construct extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation. In particular, we determine the ground state energy as a function of charges and moduli. We find that the mass of the non-BPS black hole remains that of a marginal bound state of four basic constituents throughout the entire moduli space and that there is always a non-zero gap above the BPS bound.
A sequence of zero-temperature black-hole spacetimes with angular momentum and electric and magnetic charges is shown to exist in gauged $N=2$ supergravity. Stability of a subset of these spacetimes is demonstrated by saturation of the Bogomol'nyi bound arising from the supersymmetry algebra. The mass of the resulting solitonic black holes is given in terms of the cosmological constant and the angular momentum. We conjecture that at the quantum level these solitons are dyons with angular momentum determined by the electric and magnetic charges.
We reviewed the field redefinition approach of Seeley-DeWitt expansion for the determination of Seeley-DeWitt coefficients from arXiv:1505.01156. We apply this approach to compute the first three Seeley-DeWitt coefficients for \say{non-minimal} $\mathcal{N}=1$ Einstein-Maxwell supergravity in four dimensions. Finally, we use the third coefficient for the computation of the logarithmic corrections to the Bekenstein-Hawking entropy of non-extremal black holes following arXiv:1205.0971. We determine the logarithmic corrections for non-extremal Kerr-Newman, Kerr, Reissner-Nordström and Schwarzschi…
We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS$_2 \times$S$^2$ (or other Riemann surface) preserves half of the supercharges in $N=2$ supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture. Depending o…
Motivated by the recently found 4-dimensional omega-deformed gauge supergravity, we investigate the black hole solutions within all the single scalar field consistent truncations of this theory. We construct black hole solutions that have spherical, toroidal, and hyperbolic horizon topology. The scalar field is regular everywhere outside the curvature singularity and the stress-energy tensor satisfies the null energy condition. When the parameter omega does not vanish, there is a degeneracy in the spectrum of black hole solutions for boundary conditions that preserve the asymptotic Anti-de Sit…
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 show a uniqueness theorem for charged rotating black holes in the bosonic sector of five-dimensional minimal supergravity. More precisely, under the assumptions of the existence of two commuting axial isometries and spherical topology of horizon cross-sections, we prove that an asymptotically flat, stationary charged rotating black hole with finite temperature in five-dimensional Einstein-Maxwell-Chern-Simons theory is uniquely characterized by the mass, charge, and two independent angular momenta and therefore is described by the five-dimensional Cvetic-Youm solution with equal charges. We…
We consider the non-extremal, charged, rotating black hole solution of five dimensional minimal gauged supergravity of Cvetic, Lu and Pope [Phys.Lett. B 598 (2004) 273]. We compute the Ashtekar-Magnon-Das mass and show it agrees with the thermodynamic mass. We find a reducible Killing tensor and integrate the geodesic equation explicitly. We also compute the Euclidean action of the black hole and show it satisfies the quantum statistical relation. Further we present a Smarr relation. We end with a discussion of applications to string theory.
Black hole solutions of supergravity theories form families that realizing the deep nonlinear "duality" symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e. BPS) solutions at the limits of such orbits. An important technique in the analysis of such solution families employs timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. Families of extremal or BPS solutions are characterized by nilpotent orbits under the duality symmetries, based upon a tri-graded or penta-graded decomp…
We examine five-dimensional $\mathcal N=2$ gauged supergravity including terms up to four derivatives. These additional terms correspond to the supersymmetric completion of $R^2$, and were originally obtained in hep-th/0611329 using conformal supergravity techniques. Here we integrate out the auxiliary fields and obtain the on-shell action for minimal supergravity with such corrections. We then construct $R$-charged AdS black holes to linear order in the four derivative terms and investigate the effect of these corrections on their thermodynamical properties. Finally, we relate the geometrical…
We examine the dual conformal field theory for extremal charged black holes in five-dimensional minimal supergravity with 2 independent angular momenta. The conformal field theory Virasoro algebra, central charge, and temperature are calculated. Additionally the conformal field theory entropy is calculated using the Cardy formula and agrees with the Bekenstein-Hawking black hole entropy. The central charges are directly proportional to the angular momentum components of the black hole. In five and higher dimensions, rotations of the spacetime correspond to rotations of the central charges lead…
In this paper, we consider the charged non-extremal black hole at five dimensional N = 2 supergravity. We study thermodynamics of AdS_{5} black hole with three equal charges (q_{1} = q_{2} = q_{3} = q). We obtain Schrodinger like equation and discuss the effective potential. Then, we consider the case of the perturbed dilaton field background and find presence of odd coefficients of the wave function. Also we find that the higher derivative corrections have no effect on the first and second even coefficients of the wave function.
We find U(1)_{E} \times U(1)_{M} non-extremal black hole solutions of 6-dimensional Kaluza-Klein supergravity theories. Extremal solutions were found by Cvetič and Youm\cite{C-Y}. Multi black hole solutions are also presented. After electro-magnetic duality transformation is performed, these multi black hole solutions are mapped into the the exact solutions found by Horowitz and Tseytlin\cite{H-T} in 5-dimensional string theory compactified into 4-dimensions. The massless fields of this theory can be embedded into the heterotic string theory compactified on a 6-torus. Rotating black hole solut…
In this article we study a family of four-dimensional, $\mathcal{N}=2$ supergravity theories that interpolates between all the single dilaton truncations of the $\mathrm{SO}(8)$ gauged $\mathcal{N}=8$ supergravity. In this infinitely many theories characterized by two real numbers -- the interpolation parameter and the dyonic "angle" of the gauging -- we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supers…
Supersymmetric black holes in five-dimensional gauged supergravity must necessarily be rotating, and so in order to study the passage to black holes away from supersymmetry, it is of great interest to obtain non-extremal black holes that again have non-zero rotation. In this paper we find a simple framework for describing non-extremal rotating black holes in five-dimensional gauged supergravities. Using this framework, we are able to construct a new solution, describing the general single-charge solution of N=2 gauged supergravity, with arbitrary values for the two rotation parameters. Previou…
We continue the effort of defining and evaluating the quantum entropy function for supersymmetric black holes in 4d ${\cal N} = 2$ gauged supergravity, initiated in [1803.05920]. The emphasis here is on the missing steps in the previous localization analysis, mainly dealing with one-loop determinants for abelian vector multiplets and hypermultiplets on the non-compact space $\mathbb{H}_2 \times Σ_{\rm g}$ with particular boundary conditions. We use several different techniques to arrive at consistent results, which have a most direct bearing on the logarithmic correction terms to the Bekenstei…
We extend previous investigations on the construction of extremal supersymmetric and non-supersymmetric solutions in the H-FGK formalism to "unconventional" solutions with anharmonic terms. We show how the use of "fake" charge vectors equivariant under duality transformations simplifies and clarifies the task of identification of the attractors of the theory.
We investigate the existence of supersymmetric static dyonic black holes with spherical horizon in the context of N= 2 U(1) gauged supergravity in four dimensions. We analyze the conditions for their existence and provide the general first-order flow equations driving the scalar fields and the metric warp factors from the asymptotic AdS4 geometry to the horizon. We work in a general duality-symmetric setup, which allows to describe both electric and magnetic gaugings. We also discuss the attractor mechanism and the issue of moduli (de-)stabilization.
N=8 supergravity has a rich spectrum of black holes charged under the 56 U(1) gauge fields of the theory. Duality predicts that the entropy of these black holes is related to the quartic invariant of the E(7,7) group. We verify this prediction in detail by constructing black holes that correspond to supersymmetric bound states of 2-branes at angles and 6-branes. The general bound state contains an arbitrary number of branes rotated relative to each other, and we derive the condition for these rotations to preserve supersymmetry. The microscopic bound state degeneracy matches the black hole ent…
We continue the analysis of BPS bounds started in arXiv:1110.2688, extending it to the full class of N=2 gauged supergravity theories with arbitrary vector and hypermultiplets. We derive the general form of the asymptotic charges for asymptotically flat (M_4), anti-de Sitter (AdS_4), and magnetic anti-de Sitter (mAdS_4) spacetimes. Some particular examples from black hole physics are given to explicitly demonstrate how AdS and mAdS masses differ when solutions with non-trivial scalar profiles are considered.
Based on special geometry, we consider corrections to N=2 extremal black-hole solutions and their entropies originating from higher-order derivative terms in N=2 supergravity. These corrections are described by a holomorphic function, and the higher-order black-hole solutions can be expressed in terms of symplectic Sp(2$n$+2) vectors. We apply the formalism to N=2 type-IIA Calabi-Yau string compactifications and compare our results to recent related results in the literature.
In this talk I review both accomplished results and work in progress on the use of solvable Lie algebras as an intrinsic algebraic characterization of the scalar field sector of M--theory low energy effective lagrangians. In particular I review the application of these techniques in obtaining the most general form of BPS black hole solutions.
We study one-loop covariant effective action of \say{non-minimally coupled} $\mathcal{N}=1$, $d=4$ Einstein-Maxwell supergravity theory by heat kernel tool. By fluctuating the fields around the classical background, we study the functional determinant of Laplacian differential operator following Seeley-DeWitt technique of heat kernel expansion in proper time. We then compute the Seeley-DeWitt coefficients obtained through the expansion. A particular Seeley-DeWitt coefficient is used for determining the logarithmic correction to Bekenstein-Hawking entropy of extremal black holes using quantum e…
The issue of microstate counting for general black holes in D=5, N=2 supergravity coupled to vector multiplets is discussed from various viewpoints. The statistical entropy is computed for the near-extremal case by using the central charge appearing in the asymptotic symmetry algebra of AdS_2. Furthermore, we show that the considered supergravity theory enjoys a duality invariance which connects electrically charged black holes and magnetically charged black strings. The near-horizon geometry of the latter turns out to be AdS_3 x S^2, which allows a microscopic calculation of their entropy usi…
We consider general black holes in D=5, N=2 supergravity coupled to vector multiplets, and discuss the issue of microstate counting from various viewpoints. The statistical entropy is computed for the near-extremal case using the central charge of the $AdS_2$ factor appearing in the near-horizon geometry. Furthermore, we explicitly construct the duality transformation connecting electrically charged black holes to magnetically charged black strings, under which the $AdS_2 \times S^3$ near horizon geometry becomes $AdS_3 \times S^2$. For $AdS_3$ the counting of microstates correctly reproduces …
In this paper we investigate the attractor mechanism in the five dimensional low energy supergravity theory corresponding to M-theory compactified on a Calabi-Yau threefold $CY_3$. Using very special geometry, we derive the general first-order attractor flow equations for BPS and non-BPS solutions in five-dimensional Gibbons-Hawking spaces. Especially, considering the supersymmetric solution, we obtain the first-order flow equations for supersymmetric (multi)black rings. We also solve the flow equations and discuss some properties of the solutions of flow equations.
We study the one-loop corrections to the effective on-shell action of N=2 supergravity in the background of the Reissner-Nordstrom black hole. In the extreme case the contributions from graviton, gravitino and photon to the one-loop corrections to the entropy are shown to cancel. This gives the first explicit example of the supersymmetric non-renormalization theorem for the on-shell action (entropy) for BPS configurations which admit Killing spinors. We display the residual supersymmetry of the perturbations of a general supersymmetric theory in a bosonic BPS background.
We construct the general solution for non-extremal charged rotating black holes in five-dimensional minimal gauged supergravity. They are characterised by four non-trivial parameters, namely the mass, the charge, and the two independent rotation parameters. The metrics in general describe regular rotating black holes, providing the parameters lie in appropriate ranges so that naked singularities and closed timelike curves (CTC's) are avoided. We calculate the conserved energy, angular momenta and charge for the solutions, and show how supersymmetric solutions arise in a BPS limit. These have n…
We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS$_4 \times S^6$ from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional $\mathcal{N}=2$ Chern-Simons-matter gauge theories in the large $N$ limit. The $\mathcal{I}$-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic $\mathcal{N}=2$ gauged supergravit…
