We study the index of 4d $\mathcal{N}=4$ Yang-Mills theory with $U(N)$ gauge group, focussing on the physics of the dual BPS black holes in $AdS_5\times S^5$. Certain aspects of these black holes can be studied from finite $N$ indices with reasonably large $N^2$. We make numerical studies of the index for $N\leq 6$, by expanding it up to reasonably high orders in the fugacity. The entropy of the index agrees very well with the Bekenstein-Hawking entropy of the dual black holes, say at $N^2=25$ or $36$. Our data clarifies and supports the recent ideas which allowed analytic studies of these black holes from the index, such as the complex saddle points of the Legendre transformation and the oscillating signs in the index. In particular, the complex saddle points naturally explain the $\frac{1}{N}$-subleading oscillating patterns of the index. We also illustrate the universality of our ideas by studying a model given by the inverse of the MacMahon function.
We continue the study of 3d ${\mathcal N}=2$ Chern-Simons (CS) quiver gauge theories on $Σ_{\mathfrak{g}}\times S^1$. Using localization results, we compute the twisted index of recently constructed SCFTs in the large rank limit. According to AdS/CFT correspondence, this field theory computation gives a prediction for two quantities corresponding to their holographic duals: the volumes of certain 7-dimensional Sasaki-Einstein manifolds and the entropy of black holes in $\text{AdS}_4\times Y_7$.
We discuss the large $N$ factorization properties of five-dimensional supersymmetric partition functions for CFT with a holographic dual. We consider partition functions on manifolds of the form $\mathcal{M}= \mathcal{M}_3 \times S^2_ε$, where $ε$ is an equivariant parameter for rotation. We show that, when $\mathcal{M}_3$ is a squashed three-sphere, the large $N$ partition functions can be obtained by gluing elementary blocks associated with simple physical quantities. The same is true for various observables of the theories on $\mathcal{M}_3=Σ_\mathfrak{g} \times S^1$, where $Σ_\mathfrak{g}$…
We calculate the superconformal indices of a class of six-dimensional ${\cal N}=(1,0)$ superconformal field theories realized on M5-branes at $\mathbb{C}^2/\mathbb{Z}_k$ singularity by using the method developed in previous works of the authors and collaborators. We use the AdS/CFT correspondence, and finite $N$ corrections are included as the contribution of M2-branes wrapped on two-cycles in $S^4/\mathbb{Z}_k$. We confirm that the indices are consistent with the expected flavor symmetries.
We study the large $N$ limit of the refined topologically twisted index of three-dimensional $\mathcal{N} = 2$ gauge theories with a holographic dual, which is relevant for counting the number of microstates of rotating, magnetically charged and twisted AdS$_4$ black holes. As a difference with previous computations, we perform a direct saddle point analysis of the relevant matrix model. Among other things we explicitly identify the distribution of gauge magnetic fluxes that contributes at large $N$. The index exhibits a large $N$ factorized form in agreement with the supergravity expectations…
We calculate the scalar quasinormal modes of warped $AdS_3$ black holes analytically. We find that in general they are not in agreement with the prediction of the usual AdS/CFT correspondence. Nevertheless, for the black hole not deviating far from BTZ black hole, the quasinormal frequencies are still well consistent with AdS/CFT correspondence.
We show that the entropy of D--dimensional Schwarzschild black holes are given by the entanglement entropy of a boundary of global $AdS_2$ space that lives at asymptotic infinity. We dimensionally reduce General Relativity to two dimensions which leads to 2D dilatonic gravity which has black hole solutions with the same thermodynamics as D--dimensional Schwarzschild black holes. These dilatonic black holes can be transformed into certain $AdS_2$ black holes by Weyl transformations which are symmetries of the theory that preserve the thermodynamics. In the asymptotic limit, the $AdS_2$ black ho…
We find the entropy functions of supersymmetric black holes in AdS$_4$ and AdS$_6$ with electric charges and angular momenta. Extremizing these functions, one obtains the entropies and the chemical potentials of known analytic black hole solutions.
We examine the thermodynamics and stability of 5-dimensional flat anti-de Sitter (AdS) black strings, locally asymptotically anti-de Sitter spacetimes whose spatial sections are AdS black holes with Ricci flat horizons. We find that there is a phase transition for the flat AdS black string when the AdS soliton string is chosen as the thermal background. We find that this bulk phase transition corresponds to a 4-dimensional flat AdS black hole to AdS soliton phase transition on the boundary Karch-Randall branes. We compute the possibility of a phase transition from a flat AdS black string to a …
We revisit non-rotating, dyonically charged, and supersymmetric AdS$_4$ black holes, which are solutions of $\mathcal{N}=2$ gauged supergravity with vector- and hyper-multplets. Uplifting the near horizon solutions to $D=11$ supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS$_4$ black holes correspond to AdS$_2$ solutions with electric and magnetic baryonic fluxes in $D=11$ supergravity. We identify the off-shell AdS$_4$ black hole solutions with parameters of $D=11$ AdS$_2$ solutions without imposing the equations of motion. We calculate the entropy of dyonic…
We review the recent developements in the stability problem and phase diagram for asymptotically locally $AdS$ black strings. First, we quickly review the case of locally flat black string before turning to the case of locally $AdS$ spacetimes.
We revisit the microscopic description of AdS$_3$ black holes in light of recent progress on their higher dimensional analogues. The grand canonical partition function that follows from the AdS$_3$/CFT$_2$ correspondence describes BPS and nearBPS black hole thermodynamics. We formulate an entropy extremization principle that accounts for both the black hole entropy and a constraint on its charges, in close analogy with asymptotically AdS black holes in higher dimensions. We are led to interpret supersymmetric black holes as ensembles of BPS microstates satisfying a charge constraint that is no…
We investigate finite-$N$ corrections to the superconformal indices of the theories realized on M2- and M5-branes. For three-dimensional theories realized on a stack of $N$ M2-branes we calculate the finite-$N$ corrections as the contribution of extended M5-branes in the dual geometry $AdS_4\times \boldsymbol{S}^7$. We take only M5-brane configurations with a single wrapping into account, and neglect multiple-wrapping configurations. We compare the results with the indices calculated from the ABJM theory, and find agreement up to expected errors due to the multiple wrapping. For six-dimensiona…
We calculate the correction to the Bekenstein-Hawking entropy formula for five dimensional AdS-Schwarzschild black holes due to thermodynamic fluctuations. The result is then compared with the boundary gauge theory entropy corrections via AdS/CFT correspondence. We then further generalise our analysis for the rotating black hole in five dimensional AdS space.
We show that the Abelian Higgs field equations in the background of the four dimensional AdS-Schwarzschild black hole have a vortex line solution. This solution, which has axial symmetry, is a generalization of the AdS spacetime Nielsen-Olesen string. By a numerical study of the field equations, we show that black hole could support the Abelian Higgs field as its Abelian hair. Also, we conside the self gravity of the Abelian Higgs field both in the pure AdS spacetime and AdS-Schwarzschild black hole background and show that the effect of string as a black hole hair is to induce a deficit angle…
We provide a unifying entropy functional and an extremization principle for black holes and black strings in AdS$_4\times S^7$ and AdS$_5\times S^5$ with arbitrary rotation and generic electric and magnetic charges. This is done by gluing gravitational blocks, basic building blocks that are directly inspired by the holomorphic blocks appearing in the factorization of supersymmetric partition functions in three and four dimensions. We also provide an explicit realization of the attractor mechanism by identifying the values of the scalar fields at the horizon with the critical points of the entr…
Some ones have showed the first-order phase transition of the Horava-Lifshitz (HL) AdS black holes has unique characters from other AdS black holes. While the coexistence zone of the first-order phase transition was not exhibited. As well known the coexistence curve of a black hole carries a lot of information about black hole, which provides a powerful diagnostic of the thermodynamic properties on black hole. We study the first-order phase transition coexistence curves of the HL AdS black holes by the Maxwell's equal-area law, and give the boundary of two-phase coexistence zone. It is very in…
We develop the thermodynamics of black holes in AdS$_4$ and AdS$_7$ near their BPS limit. In each setting we study the two distinct deformations orthogonal to the BPS surface as well as their nontrivial interplay with each other and with BPS properties. Our results illuminate recent microscopic calculations of the BPS entropy. We show that these microscopic computations can be leveraged to also describe the near BPS regime, by generalizing the boundary conditions imposed on states.
We compute logarithmic corrections to the entropy of a magnetically charged extremal black hole in AdS4 x S7 using the quantum entropy function and discuss the possibility of matching against recently derived microscopic expressions.
We consider a D5-brane solution in AdS black hole spacetime. This is a defect solution moving in subspace of AdS5 x S5. This non-local object is realized by the probe D5-brane moving in black hole spacetime. We found this probe brane does not penetrate the black hole horizon. We also found the solution does not depend on the motion on S5 subspace.
We investigate the superconformal indices for the Chern-Simons-matter theories proposed for M2-branes probing the cones over N^{010}/Z_k, Q^{111}, M^{32} with N=2,3 supersymmetries and compare them with the corresponding dual gravity indices. For N^{010}, we find perfect agreements. In addition, for N^{010}/Z_k, we also find an agreement with the gravity index including the contributions from two types of D6-branes wrapping RP^3. For Q^{111}, we find that the model obtained by adding fundamental flavors to the N=6 theory has the right structure to be the correct model. For M^{32}, we find the …
We claim that there is a one to one correspondence between $NAdS_2$ spacetimes and dilatonic $AdS_2$ black holes. We show that these have the same thermodynamics and can be described by the same states of 1D CFTs with the same central charge. In addition, we show that these are actually the same set of solutions since a field redefinition in the Schwarzian theory transforms its equation of motion into the time independent part of the bulk Einstein equation. The deformations of the $AdS_2$ boundary as a function of the boundary time are exactly the conformal factor of the $AdS_2$ black hole met…
Conformal mechanics related to the near horizon extreme Kerr-Newman-AdS-dS black hole is studied. A unique N=2 supersymmetric extension of the conformal mechanics is constructed.
We consider computational complexity of AdS_5 black holes. Our system contains a particle moving on the boundary of AdS. This corresponds to the insertion of a fundamental string in AdS_5 bulk spacetime. Our results give a constraint for complexity. This gives us a hint for defining complexity in quantum field theories.
An AdS_2 black hole spacetime is an AdS_2 spacetime together with a preferred choice of time. The Boulware, Hartle-Hawking and SL(2,R) invariant vacua are constructed, together with their Green functions and stress tensors, for both massive and massless scalars in an AdS_2 black hole. The classical Bekenstein-Hawking entropy is found to be independent of the temperature, but at one loop a non-zero entanglement entropy arises. This represents a logarithmic violation of finite-temperature decoupling for AdS_2 black holes which arise in the near-horizon limit of an asymptotically flat black hole.…
We present a new method for reconstructing CFT duals of states excited by the bulk local operators in the three dimensional AdS black holes in the AdS/CFT context. As an important procedure for this, we introduce a map between the bulk points in AdS and those on the boundary where CFT lives. This gives a systematic and universal way to express bulk local states even inside black hole interiors. Our construction allows us to probe the interior structures of black holes purely from the CFT calculations. We analyze bulk local states in the single-sided black holes as well as the double-sided blac…
In this paper, we present an AdS black hole solution with Ricci flat horizon in Einstein-phantom scalar theory. The phantom scalar fields just depend on the transverse coordinates $x$ and $y$, and which are parameterized by the parameter $α$. We study the thermodynamics of the AdS phantom black hole. Although its horizon is a Ricci flat Euclidean space, we find that the thermodynamical properties of the black hole solution are qualitatively same as those of AdS Schwarzschild black hole. Namely there exists a minimal temperature, the large black hole is thermodynamically stable , while the smal…
In this paper, we study various aspects of the equilibrium thermodynamic state space geometry of AdS black holes. We first examine the Reissner-Nordstrom-AdS (RN-AdS) and the Kerr-AdS black holes. In this context, the state space scalar curvature of these black holes is analysed in various regions of their thermodynamic parameter space. This provides important new insights into the structure and significance of the scalar curvature. We further investigate critical phenomena, and the behaviour of the scalar curvature near criticality, for KN-AdS black holes in two mixed ensembles, introduced an…
We use the AdS/CFT correspondence to argue that large rotating black holes in global AdS(D) spaces are dual to stationary solutions of the relativistic Navier-Stokes equations on S**(D-2). Reading off the equation of state of this fluid from the thermodynamics of non-rotating black holes, we proceed to construct the nonlinear spinning solutions of fluid mechanics that are dual to rotating black holes. In all known examples, the thermodynamics and the local stress tensor of our solutions are in precise agreement with the thermodynamics and boundary stress tensor of the spinning black holes. Our…
Based on the numerical conformal bootstrap bound, we show that the arbitrarily small Reissner-Nordström black hole in AdS space-time is inconsistent with holography unless the energy spectrum is modified quantum mechanically or it is unstable as indicated by the weak gravity conjecture.
We provide a realization of the AdS$_2$/CFT$_1$ correspondence in terms of asymptotic symmetries of the AdS$_2\times$S$^1$ and AdS$_2\times$S$^2$ geometries arising in near-extremal BTZ and Reissner-Nordström black holes. Cardy's formula exactly accounts for the deviation of the Bekenstein-Hawking entropy from extremality. We also argue that this result can be extended to more general black holes near extremality.
We study black holes in AdS-like spacetimes, with the horizon given by an arbitrary positive curvature Einstein metric. A criterion for classical instability of such black holes is found in the large and small black hole limits. Examples of large unstable black holes have a Böhm metric as the horizon. These, classically unstable, large black holes are locally thermodynamically stable. The gravitational instability has a dual description, for example by using the $AdS_7 \times S^4$ version of the AdS/CFT correspondence. The instability corresponds to a critical temperature of the dual thermal f…
In this work, we study the real-time dynamics of the charged hairy black hole with the time-dependent source of scalar field in asymptotically anti-de Sitter (AdS) spacetime. The numerical results reveal a novel descalarization mechanism. In order to obtain the hairy black hole as the initial data for the quench process, we first analyze the quasi-normal modes of the massive complex scalar field on the Reissner-Nordström anti-de Sitter (RN-AdS) black hole background. We find the dominant unstable modes for large and small RN-AdS black holes come from the zero-damped modes and AdS modes, respec…
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 …
In a recent paper hep-th/0008140 by E. Verlinde, an interesting formula has been put forward, which relates the entropy of a conformal formal field in arbitrary dimensions to its total energy and Casimir energy. This formula has been shown to hold for the conformal field theories that have AdS duals in the cases of AdS Schwarzschild black holes and AdS Kerr black holes. In this paper we further check this formula with various black holes with AdS asymptotics. For the hyperbolic AdS black holes, the Cardy-Verlinde formula is found to hold if we choose the ``massless'' black hole as the ground s…
In this note we show that the entropy of BPS, rotating, electrically charged AdS$_7 \times S^4$ black holes can be obtained by an extremization principle involving a particular combination of anomaly coefficients of the six-dimensional $\mathcal{N} = (2, 0)$ theory. This result extends our previous finding for BPS, rotating AdS$_5 \times S^5$ black holes.
The large $N$ limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS$_5$ black holes only in the particular case of equal angular momenta. Using the Bethe Ansatz formulation, we compute the index at large $N$ with arbitrary chemical potentials for all charges and angular momenta, for general $\mathcal{N}=1$ four-dimensional conformal theories with a holographic dual. We conjecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large $N$. For $\mathcal{N}=4$ S…
We discuss the entropy for the extremal BTZ black hole and the extremal EBTZ black hole. The EBTZ black hole means the BTZ black hole embedded in a five-dimensional(5D) black hole. The six-dimensional(6D) black string with traveling waves is introduced as a concrete model for realizing the AdS/CFT correspondence. The traveling waves carry the momentum distribution $p(u)$ which plays an important role in counting the entropy and establishing the correspondence. It turns out that the EBTZ black hole is consistent with the AdS/CFT correspondence.
By using the generalized version of gauge/gravity correspondence, we study the mass spectra of several typical QCD$_4$ glueballs in the framework of AdS$_6$ black hole metric of Einstein gravity theory. The obtained glueball mass spectra are numerically in agreement with those from the AdS$7 \times S^4$ black hole metric of the 11-dimensional supergravity.
We show that the very near horizon region of nonextreme black holes, which can be described by horizon CFTs, are related to $AdS_2$ Rindler spaces. The latter are $AdS_2$ black holes with specific masses and can be described by states of either $D=1$ or $D=2$ CFTs. The central charges of these CFTs and the conformal weights of their states that correspond to the nonextreme black holes exactly match those predicted by the horizon CFTs, providing supporting evidence for this description.
We study the equations of black strings in spacetimes of arbitrary dimensions with a negative cosmological constant and construct numerically non uniform black strings solutions. Our results suggest the existence of a localised black hole in asymptotically locally $AdS$ spacetime. We also present evidences for a dependence of the critical dimension on the horizon radius.The critical dimension represents the dimension where the order of the phase transition between uniform and non uniform black string changes. Finally, we argue that both, the regular asymptotically locally $AdS$ solution and $A…
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 …
Motivated by recent studies of supersymmetric black holes, we revisit the phase diagram of AdS black holes, whether BPS or not, with particular emphasis on the role of rotation. We develop BPS thermodynamics systematically and, in many explicit examples, we study its striking similarities with more familiar AdS black holes, as well as some differences. We highlight an important fugacity that preserves BPS saturation but is not captured by the supersymmetric index.
We calculate analytically low frequency quasi-normal modes of gravitational perturbations of AdS Schwarzschild black holes in $d$ dimensions. We arrive at analytic expressions which are in agreement with their counterparts from linearized hydrodynamics in $S^{d-2}\times \mathbb{R}$, in accordance with the AdS/CFT correspondence. Our results are also in good agreement with results of numerical calculations.
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…
We show that there exists a precise kinematical notion of holography for the Euclidean warped $AdS_3$ black hole. This follows from the fact that the Euclidean warped $AdS_3$ black hole spacetime is a geometrically finite hyperbolic manifold. For such manifolds a theorem of Sullivan provides a one-to-one correspondence between the hyperbolic structure in the bulk and the conformal structure of its boundary. Using this theorem we obtain the holographic quasinormal modes for the warped $AdS_3$ black hole.
We consider the entropy problem of AdS_3 black holes using the conformal field theory at the horizon. We observe that the supersymmetry is enhanced at the horizon of massless AdS_3 black hole. This allows us to determine the vacuum of the modular invariant conformal field theory to be the NS-ground state (which corresponds to AdS_3 spacetime). This is smoothly related to the R-ground state (corresponding to massless black hole) by a spectral flow, which can be understood as a superconformal transformation.
In this work we consider a spacial kind of spacetime called AdS accelerating black holes. This is a kind of black holes which contain a stringlike singularity along polar axises attached to the black hole and it accelerates the black hole. By using a string as a probe we study the properties of complexity growth of black holes following the CA duality. Our result is the growth of complexity is independent of acceleration but the string probe detects the effects of acceleration.
It is demonstrated that the near-horizon geometry of general non-extremal black holes can be described by a portion of AdS space. We show that the reason why hidden conformal symmetries near horizons of general non-extremal black holes are achieved in previous works is that the near-horizon geometries have been equivalently taken as these AdS segments rather than simply the Rindler space.
We study black hole solutions in extended gravities with higher-order curvature terms, including conformal and Einstein-Weyl gravities. In addition to the usual AdS vacuum, the theories admit Lifshitz and Schrödinger vacua. The AdS black hole in conformal gravity contains an additional parameter over and above the mass, which may be interpreted as a massive spin-2 hair. By considering the first law of thermodynamics, we find that it is necessary to introduce an associated additional intensive/extensive pair of thermodynamic quantities. We also obtain new Liftshitz black holes in conformal grav…
The two-dimensional anti-de Sitter space(AdS_2) is constructed in terms of the CGHS model. The geometric solutions are composed of the AdS vacuum and the AdS black hole which are locally equivalent but distinguishable by their mass. The infalling classical fields do not play any role but the quantum back reaction is crucial in the formation of the AdS vacuum and AdS black hole. In the presence of the AdS black hole, there does not exist any radiation, which is consistent with the constraint equations. Therefore the transition from the AdS black hole to the AdS vacuum is impossible, and they ar…
In this letter we propose a new ansatz for the thermal string in the TFD formulation. From it, we derive the thermal vacuum for the closed bosonic string and calculate the thermal partition function in the blackhole $AdS$ background in the first order of the perturbative quantization.
We construct the non uniform AdS black string solution with a perturbation theory in six dimensions, focusing on the backreacting second order correction. The backreactions at second order give the first relevant corrections to the thermodynamical quantities. Our results show that for configurations with horizon radius and length in the extradimension small compared to the AdS radius, the properties of the non uniform black string are similar to the locally asymptotically flat case. For black strings with small horizon radial coordinate but large length in the extradimension, the thermodynamic…
Motivated by a recent work on asymptotically AdS_4 black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2 and M5-branes. Concretely, we consider AdS black holes in AdS_{p+2}\times S^{11-p-2}, where p=2,5 by interpreting the number of M2 (and M5-branes) as a thermodynamical variable. We study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then, we compute the thermodynamical curvatures from the Quevedo metric for M2 and M…
We present a detailed discussion of AdS_3 black holes and their connection to two-dimensional conformal field theories via the AdS/CFT correspondence. Our emphasis is on deriving refined versions of black hole partition functions, that include the effect of higher derivative terms in the spacetime action as well as non-perturbative effects. We include background material on gravity in AdS_3, in the context of holographic renormalization.
We utilize the classification of IIB horizons with 5-form flux to present a unified description for the geometry of AdS_n, n=3,5,7 solutions. In particular, we show that all such backgrounds can be constructed from 8-dimensional 2-strong Calabi-Yau geometries with torsion which admit some additional isometries. We explore the geometry of AdS_3 and AdS_5 solutions but we do not find AdS_7 solutions.
The phase transition of the Gauss-Bonnet AdS black hole has the similar property with the van der Waals thermodynamic system. However, it is determined by the Gauss-Bonnet coefficient α, not only the horizon radius. Furthermore, the phase transition is not the pure one between a big black hole and a small black hole. With this issue, we introduce a new order parameter to investigate the critical phenomenonand to give the microstructure explanation of the Gauss-Bonnet AdS black hole phase transition. And the critical exponents are also obtained. At the critical pointof the Gauss-Bonnet AdS blac…
In these lectures I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimensions equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS$_4$ black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS$_5$ black holes.
