We study the stability of AdS black hole holes rotating in a single two plane for tensor-type gravitational perturbations in $D > 6$ space-time dimensions. First, by an analytic method, we show that there exists no unstable mode when the magnitude $a$ of the angular momentum is smaller than $r_h^2/R$ where $r_h$ is the horizon radius, and $R$ is the AdS curvature radius. Then, by numerical calculations of quasinormal modes, using the separability of the relevant perturbation equations, we show that an instability occurs for rapidly rotating black holes with $a>r_h^2/R$, although the growth rate is tiny (of order $10^{-12}$ of the inverse horizon radius). We give numerical evidences indicating that this instability is caused by superradiance.
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.
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.
We study solutions for rigidly rotating strings on AdS$_4 \times$ CP$^3$ in the presence of $B_{\rm NS}$ holonomy turned on over $CP^1 \subset CP^3$. We construct general solutions for rotating strings with two and three angular momenta in $CP^3$ and discuss various limits corresponding to giant magnon and spike like solutions.
Semi-classical soliton solutions for superstrings in $AdS_5\times S^5$ are used to predict the dimension of gauge theory operators in $\N=4 $ SU(N) SYM theory. We discuss the possible origin of scaling violations on the gauge theory side.
We study rigidly rotating strings in the $\varkappa$-deformed $AdS_3 \times S^3$ background. We find out two classes of solutions corresponding to the giant magnon and single spike solutions of the string rotating in two $S^2_{\varkappa}$ subspace of rotations reduced along two different isometries. We verify that the dispersion relations reduce to the well known relation in the $\varkappa\rightarrow 0$ limit. We further study some oscillating string solutions in the $S^3_{\varkappa}$ subspace.
Rotating IIB strings in AdS_5 x S^5 become ultra-relativistic, and hence effectively tensionless, in the limit of large angular momentum on S^5. We have shown previously that such tensionless strings may preserve supersymmetry. Here we extend this result to include a class of supersymmetric tensionless strings with arbitrary SO(6) angular momentum. We close with some general comments on tensionless strings in AdS_5 x S^5.
We probe the AdS/CFT correspondence by comparing the thermodynamics of a rotating black hole in five-dimensional anti-de Sitter space with that of a conformal field theory on $S^3$, whose parameters come from the boundary of spacetime. In the high temperature limit, we find agreement between gauge theory and gravity in all thermodynamic quantities upto the same factor of 4/3 that appears for nonrotating holes.
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…
It is shown that a class of rotating strings in AdS_5 x S^5 with SO(6) angular momenta (J,J',J') preserve 1/8-supersymmetry for large J,J', in which limit they are effectively tensionless; when J=0, supersymmetry is enhanced to 1/4. These results imply that recent checks of the AdS/CFT correspondence actually test a nearly-BPS sector.
We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS$_5\times S^5$ can be obtained by a simple extremization principle. We expect that this extremization corresponds to the attractor mechanism for BPS rotating black holes in five-dimensional gauged supergravity, which is still unknown. The expression to be extremized has a suggestive resemblance to anomaly polynomials and the supersymmetric Casimir energy recently studied for $\mathcal{N}=4$ super Yang-Mills.
A comparison is made between the thermodynamics of weakly and strongly coupled Yang-Mills with fixed angular momentum. The free energy of the strongly coupled Yang-Mills is calculated by using a dual supergravity description corresponding to a rotating black hole in an Anti de Sitter (AdS) background. All thermodynamic quantities are shown have the same ratio of 3/4 (independent of angular momentum) between strong and weak coupling.
Rotating charged Gauss-Bonnet black hole solutions in higher dimensional ($d >4$), asymptotically anti-de Sitter spacetime are obtained in the small angular momentum limit. The angular momentum, magnetic dipole moment, and the gyromagnetic ratio of the black holes are calculated and it turns out that the Gauss-Bonnet term does not affect to the gyromagnetic ratio.
In this paper, we study the spin chain and string excitation in the rotating Rindler-$AdS_3$ proposed in [12]. We obtain a one-parameter deformed $SL(2)$ spin chain at the fast spin limit. Two-spin GKP-like solutions are studied at short and long string limits. General ansatz for the giant magnons and the spiky strings are analyzed in detail for various $β$. At last, we explore its counterpart in analytic continuation and pp-wave limit.
In this paper we study the classical dynamics of long strings in AdS3, generalizing our previous study, arXiv:1410.3424 [hep-th], to rotating strings and BTZ black holes. As in the non-rotating case, BTZ black holes are generated in the large tension limit, in which string back-reaction must be taken into account. When back-reaction is properly accounted for, collapsing heavy, physical, rotating strings do not generate naked singularities but only BTZ black holes, including extremal ones. The rotating string must contain world-sheet excitations in order to have consistent equations of motion; …
Motivated by the recent progress on gravity duals of supersymmetric Chern-Simons matter theories, we consider classical membrane solutions in AdS_4 x M^{1,1,1}. In particular, we present several types of exact solutions rotating in the Sasaki-Einstein 7-manifold whose isometry is SU(3)xSU(2)xU(1). We analyze the limiting behavior of macroscopic membranes and discuss how one can identify the dual operators and the implications of our result on their conformal dimensions.
We study semiclassical rotating strings in AdS/CFT backgrounds that exhibit both confinement and finite-size effects. The energy versus spin dispersion relation for short strings is the expected Regge trajectory behaviour, with the same string tension as is measured by the Wilson loop. Long strings probe the interplay between confinement and finite-size effects. In particular, the dispersion relation for long strings shows a characteristic dependence on the string tension and the finite-size scale.
We derive a class of charged rotating dilaton black string solutions in the background of anti-de-Sitter spaces with an appropriate combination of three Liouville-type dilaton potentials. We also present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. The solutions are analyzed and their thermodynamics is discussed by using the counterterm method.
We analyze stationary BPS black hole solutions to 4d $\mathcal{N}=2$ abelian gauged supergravity. Using an appropriate near horizon ansatz, we construct rotating attractors with magnetic flux realizing a topological twist along the horizon surface, for any theory with a symmetric scalar manifold. An analytic flow to asymptotically locally $AdS_4$ is presented for a subclass of these near horizon geometries, and an explicit new example of supersymmetric $AdS_4$ rotating black hole is discussed in detail. We further note that, upon tuning the gauging to special values, one can obtain solutions w…
We classify the necessary and sufficient conditions to obtain the near-horizon geometry of extremal supersymmetric rotating black holes embedded in 11d supergravity. Such rotating black holes admit an AdS$_2$ near-horizon geometry which is fibered by the transverse spacetime directions. Despite their clear interest to understanding the entropy of rotating black holes, these solutions have evaded all previous supersymmetric classification programs due to the non-trivial fibration structure. In this paper we allow for the most general fibration over AdS$_2$ with a flux configuration permitting r…
Extremal black holes have vanishing Hawking temperatures. In this article, we argue that for asymptotically AdS black holes, at extremality, a particular class of correlators in the dual CFT can exhibit exponential, maximally chaotic growth with a non-vanishing temperature. Our approach, at extremality, is two-fold. First, we geometrically investigate the modes that are responsible for chaos. Secondly, we study the dynamics of a probe string to capture chaos in worldsheet correlators. For rotating BTZ at extremality, the corresponding Lyapunov exponent is determined by the left-moving temperat…
We investigate the near-horizon limit of extremally rotating NS5-branes. The resulting geometry has SL(2,R) \times U(1)^2 isometry. The asymptotic symmetry group contains a chiral Virasoro algebra, and we obtain two different realizations depending on the boundary conditions we impose. When one of the two angular momenta vanishes, the symmetry is enhanced to AdS_3. The entropy of the boundary theory can be estimated from the Cardy formula and it agrees with the Bekenstein-Hawking entropy of the bulk theory. We can embed the extremally rotating NS5-brane geometry in an exactly solvable string b…
We discuss quantum fluctuations of a class of rotating strings in AdS_5 x S^5. In particular, we develop a systematic method to compute the one-loop sigma-model effective actions in closed forms as expansions for large spins. As examples, we explicitly evaluate the leading terms for the constant radii strings in the SO(6) sector with two equal spins, the SU(2) sector, and the SL(2) sector. We also obtain the leading quantum corrections to the space-time energy for these sectors.
We study rigidly rotating and pulsating $(m,n)$ strings in $AdS_3 \times S^3$ with mixed three form flux. The $AdS_3 \times S^3$ background with mixed three form flux is obtained in the near horizon limit of $SL(2,Z)$-transformed solution, corresponding to the bound state of NS5-branes and fundamental strings. We study the probe $(m,n)-$string in this background by solving the manifest $SL(2,Z)-$covariant form of the action. We find out the dyonic giant magnon and single spike solutions corresponding to the equations of motion of a probe string in this background and find out various relations…
We present arguments for the existence of charged, rotating black holes with equal magnitude angular momenta in $d=5$ Einstein-Yang-Mills theory with negative cosmological constant. These solutions posses a regular horizon of spherical topology and approach asymptotically the Anti-de Sitter spacetime background. The black hole solutions have also an electric charge and a nonvanishing magnetic flux through the sphere at infinity. Different from the static case, no regular solution with a nonvanishing angular momenta is found for a vanishing event horizon radius.
In the context of AdS/CFT we provide analytical support for the proposed duality between a Wilson loop with a cusp, the cusp anomalous dimension, and the meson model constructed from a rotating open string with high angular momentum. This duality was previously studied using numerical tools in [1]. Our result implies that the minimum of the profile function of the minimal area surface dual to the Wilson loop, is related to the inverse of the bulk penetration of the dual string that hangs from the quark--anti-quark pair (meson) in the gauge theory.
In this paper we consider a quark-antiquark ($q\bar{q}$) pair which can be interpreted as a meson in ${\mathcal{N}}$=4 SYM thermal plasma. We assume that the string moves at speed $v$ and rotates around its center of mass simultaneously. By using the AdS/CFT correspondence, we obtain the momentum densities of the rotating string and determine its motion for small angular velocities. Then in general case, we calculate the screening length of $q\bar{q}$ pair numerically and show that its velocity dependance is in consistent with the well known formula $L_s T\sim (1-v^{2})^{1/4}$ in the literatur…
We consider rotating, electrically charged, supersymmetric AdS black holes in four, five, six and seven dimensions, and provide a derivation of the respective extremization principles stating that the Bekenstein-Hawking entropy is the Legendre transform of a homogeneous function of chemical potentials, subject to a complex constraint. Extending a recently proposed BPS limit, we start from finite temperature and reach extremality following a supersymmetric trajectory in the space of complexified solutions. We show that the entropy function is the supergravity on-shell action in this limit. Chem…
We provide a general formula for the refined topologically twisted index of $\mathcal{N}=1$ gauge theories living on the world-volume of D3-branes at conical Calabi-Yau singularities in the Cardy limit. The index is defined as the partition function on $T^2 \times S^2_ω$, with a partial topological twist and a $Ω$-deformation along $S^2$, in the presence of background magnetic fluxes and fugacities for the global symmetries and can be used to study the properties of a class of BPS black strings. To this purpose, we find rotating domain-wall solutions of five-dimensional gauged supergravity int…
We present the metric for the $(n+1)$-dimensional charged rotating dilaton black branes with cylindrical or toroidal horizons in the background of anti-de Sitter spacetime. We find the suitable counterterm which removes the divergences of the action in the presence of the dilaton potential in all higher dimensions. We plot the Penrose diagrams of the spacetime and reveal that the spacetime geometry crucially modifies in the presence of the dilaton field. The conserved and thermodynamic quantities of the black branes are also computed.
We show that one may pass from bulk to boundary thermodynamic quantities for rotating AdS black holes in arbitrary dimensions so that if the bulk quantities satisfy the first law of thermodynamics then so do the boundary CFT quantities. This corrects recent claims that boundary CFT quantities satisfying the first law may only be obtained using bulk quantities measured with respect to a certain frame rotating at infinity, and which therefore do not satisfy the first law. We show that the bulk black hole thermodynamic variables, or equivalently therefore the boundary CFT variables, do not always…
By using the non-diagonal uniform gauge for the Nambu-Goto string action we derive a gauge-fixed Hamiltonian of a square-root form for the closed string in AdS_5 x S^5 which is wound and rotating in an angular direction in S^5. From the Nambu-Goto string action using a non-diagonal gauge we construct a solution describing a wound string which rotates in the same angular direction as the winding direction. The relation between energy and angular momentum of the string solution is characterized by the winding number and the bending number, and becomes linear in the large angular momentum limit. …
Strings on $AdS_3 \times S^3\times S^3\times S^1$ with mixed flux exhibit exact integrability. We wish to construct an integrable Neumann-Rosochatius (NR) model of strings starting with the type IIB supergravity action in $AdS_3 \times S^3\times S^3\times S^1$ with pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integrals of motion of the considered system are NR-like with some suitable deformations which eventually appear due to the presence of flux. We utilize the integrable framework of the deformed NR model to analyze rigidly rotating spiky strings moving only…
We investigate the quasinormal spectrum of electromagnetic perturbations of rotating black strings. Among the solutions of Einstein equations in the presence of a negative cosmological constant there are asymptotically anti-de Sitter (AdS) black holes whose horizons have the topology of a cylinder. The stationary version of these AdS black holes represents rotating black strings. The conformal field theory (CFT) dual of a black string lives in a Minkowski space with a compact dimension. On the basis of the AdS/CFT duality, we interpret a CFT plasma moving with respect to the preferred rest fra…
We show that the rotating asymptotically anti de Sitter black hole solution of new massive gravity in three dimensions can support a static stealth configuration given by a conformally coupled scalar field. By static stealth configuration, we mean a nontrivial time independent scalar field whose energy-momentum tensor vanishes identically on the rotating black hole metric solution of new massive gravity. The existence of this configuration is rendered possible because of the presence of a gravitational hair in the black hole metric that prevents the scalar field to be trivial. In the extremal …
We show that if one chooses the Einstein Static Universe as the metric on the conformal boundary of Kerr-AdS spacetime, then the Casimir energy of the boundary conformal field theory can easily be determined. The result is independent of the rotation parameters, and the total boundary energy then straightforwardly obeys the first law of thermodynamics. Other choices for the metric on the conformal boundary will give different, more complicated, results. As an application, we calculate the Casimir energy for free self-dual tensor multiplets in six dimensions, and compare it with that of the sev…
We find the minimal energy solution describing a folded closed string located at the center of AdS_5 and rotating simultaneously in two planes in S^5 with two arbitrary SO(6) angular momenta J_1 and J_2. In the case when J_1=J_2=J' we observe the precise agreement between the leading coefficient in the large J' expansion of the energy of this solution and the minimal eigen-value of the 1-loop anomalous dimension matrix of the corresponding [J',0,J'] SYM operators obtained by Beisert, Minahan, Staudacher and Zarembo in hep-th/0306139. We find also perfect agreement between string and SYM result…
In this work we explore the effect of rotation in the size of a traversable wormhole obtained via a double trace boundary deformation. We find that at fixed temperature the size of the wormhole increases with the angular momentum $J/M\ell$. The amount of information that can be sent through the wormhole increases as well. However, for the type of interaction considered, the wormhole closes as the temperature approaches the extremal limit. We also briefly consider the scenario where the boundary coupling is not spatially homogeneous and show how this is reflected in the wormhole opening.
In the microcanonical ensemble for string theory on $ AdS_m \times S^n$, there is a phase transition between a black hole solution extended over the $S^n$ and a solution localized on the $S^n$ if the $AdS_m$ has the topology $R^2 \times S^{m-2}$. The phase transition will not appear if the $AdS_m$ has the topology $R^2 \times T^{m-2}$, that is, when the $AdS_m\times S^n$ geometry is regarded as arising from the near-horizon limit of a black $m-2$ brane. In this paper, we argue that when the black branes are rotating, the localization phase transition will occur between some rotating branes and…
By using the scaling symmetry in the reduced action formalism, we derive the novel Smarr relation which holds even for the hairy rotating AdS_3 black holes. And then, by using the Smarr relation we argue that the hairy rotating AdS_3 black holes are stable thermodynamically, compared to the non-hairy ones.
We show that the $E-S \sim \log S$ behaviour found for long strings rotating on $AdS_5\times S^5$ may be reproduced by membranes rotating on $AdS_4\times S^7$ and on a warped $AdS_5$ M-theory solution. We go on to obtain rotating membrane configurations with the same $E-K \sim \log K$ relation on $G_2$ holonomy backgrounds that are dual to ${\mathcal{N}}=1$ gauge theories in four dimensions. We study membrane configurations on $G_2$ holonomy backgrounds systematically, finding various other Energy-Charge relations. We end with some comments about strings rotating on warped backgrounds.
We construct an exact metric which at short distances is the metric of massless particles in 5+1 spacetime (moving along a diameter of the sphere) and is AdS_3\times S^3 at infinity. We also consider a set of a conical defect spacetimes which are locally AdS_3\times S^3 and have the masses and charges of a special set of chiral primaries of the dual orbifold CFT. We find that excitation energies for a scalar field in the latter geometries agree exactly with the excitations in the corresponding CFT state created by twist operators: redshift in the geometry reproduces `long circle' physics in th…
We propose a new entry within the dictionary of the AdS/CFT duality at strong coupling: in the limit of a large spin or a large R-charge, the anomalous dimension of the gauge theory operator dual to a semiclassical rotating string is proportional to the string proper length. This conjecture is motivated by a generalization to strings of the rule for computing anomalous dimensions of massive particles and supergravity fields in the anti-de Sitter space. We show that this proportionality holds for a rotating closed string in global AdS space, representing a high spin operator made of fields in t…
In this paper, we consider a charged rotating AdS black holes in four dimensions and study the effects of leading-order thermal corrections on the thermodynamics of such system explicitly. The first-order corrected thermodynamical quantities also satisfy the first-law of thermodynamics of the black holes. The holographic duality between the charged rotating AdS black holes and Van der Waals fluid is also emphasized through the $P-v$ diagram. Finally, we study the effects of the leading-order thermal corrections on the stability of the charged rotating black holes.
In this work, we study the emission of tensor-type gravitational degrees of freedom from a higher-dimensional, simply rotating black hole in the bulk. The decoupled radial part of the corresponding field equation is first solved analytically in the limit of low-energy emitted particles and low-angular momentum of the black hole in order to derive the absorption probability. Both the angular and radial equations are then solved numerically, and the comparison of the analytical and numerical results show a very good agreement in the low and intermediate energy regimes. By using our exact, numeri…
We apply the Kerr/CFT correspondence to the rotating black p-brane solutions. These solutions give the simplest examples from string theory point of view. Their near horizon geometries have structures of AdS, even though black p-brane solutions do not have AdS-like structures in the non-rotating case. The microscopic entropy which can be calculated via the Cardy formula exactly agrees with Bekenstein-Hawking entropy.
If the Hamiltonian of a quantum field theory is taken to be a timelike isometry, the vacuum state remains empty for all time. We search for such stationary vacua in anti-de Sitter space. By considering conjugacy classes of the Lorentz group, we find interesting one-parameter families of stationary vacua in three-dimensional anti-de Sitter space. In particular, there exists a family of rotating Rindler vacua, labeled by the rotation parameter beta, which are related to the usual Rindler vacuum by non-trivial Bogolubov transformations. Rotating Rindler-AdS space possesses not only an observer-de…
We consider rotating topological black branes with one rotational parameter in various dimensions. Also a general five-dimensional higher genus solution of the Einstein equation with a negative cosmological constant which represents a topological black brane with two rotational parameters is introduced. We find out that the counterterms inspired by conformal field theory introduced by Kraus, Larsen and Sieblink cannot remove the divergences in $r$ of the action in more than five dimensions. We modify the counterterms by adding a curvature invariant term to it. Using the modified counterterms w…
We investigate the stability of $D$ dimensional singly rotating Myers-Perry-AdS black holes under superradiance against scalar field perturbations. It is well known that small four dimensional rotating or charged Anti-de Sitter (AdS) black holes are unstable against superradiance instability of a scalar field. Recent works extended the existence of this instability to five dimensional rotating charged AdS black holes or static charged AdS black holes in arbitrary dimensions. In this work we analytically prove that, rotating small AdS black holes in arbitrary dimensions also show superradiance …
We generalize the vacuum static black brane solutions of Einstein's equations with negative cosmological constant recently discussed in literature, by introducing rotations and an electromagnetic field. We investigate numerically the thermodynamical properties of the charged and of the rotating $AdS$ black brane and we provide evidences for the existence of the charged and rotating case. In particular, we study the influence of the rotation and charge on the tension and mass. We find that the rotation essentially influences the tensions while the charge essentially influences the mass.
Quadratic Curvature Correction to the Euclidean Action of Rotating AdS Black Holes in General Dimensions
The International Joint Institute of Tianjin University, Fuzhou, Tianjin University（天津大学福州国际联合学院）；Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）
Using a boundary counterterm prescription motivated by the AdS/CFT conjecture, I evaluate the energy, entropy and angular momentum of the class of Kerr-NUT/bolt-AdS spacetimes. As in the non-rotating case, when the NUT charge is nonzero the entropy is no longer equal to one-quarter of the area due to the presence of the Misner string. When the cosmological constant is also non-zero, the entropy is bounded from above.
Following Gubser, Klebanov and Polyakov [hep-th/0204051], we study strings in AdS black hole backgrounds. With respect to the pure AdS case, rotating strings are replaced by orbiting strings. We interpret these orbiting strings as CFT states of large spin similar to glueballs propagating through a gluon plasma. The energy and the spin of the orbiting string configurations are associated with the energy and the spin of states in the dual finite temperature N=4 SYM theory. We analyse in particular the limiting cases of short and long strings. Moreover, we perform a thermodynamic study of the ang…
We obtain the charged rotating black hole in conformal gravity. The metric is asymptotic to the (anti-)de Sitter spacetime. The contribution to the metric from the charges has a slower falloff than that in the Kerr-Newman AdS black hole. We analyse the global structure and obtain all the thermodynamical quantities including the mass, angular momentum, electric/magnetic charges and their thermodynamical conjugates. We verify that the first law of thermodynamics holds. We also obtain the new neutral rotating black holes that are beyond Einstein metrics. In contrast to the static ones, these rota…
We find that the Kerr-(Newman)-AdS$_4$ black hole will be shadowless if its rotation parameter is larger than a critical value and the shadowless-ness may be related to the appearance of the null hypersurface caustics (NHC) both inside the Cauchy horizon and outside the event horizon for the black hole with the rotation parameter beyond the critical value. Our studies also further confirm that whether an ultraspinning black hole is super-entropic or not is unrelated to the existence of the NHC outside the event horizon.
Using the null-geodesic tunneling method of Parikh and Wilczek, we derive the Hawking temperature of a general four-dimensional rotating black hole. In order to eliminate the motion of $ϕ$ degree of freedom of a tunneling particle, we have chosen a reference system that is co-rotating with the black hole horizon. Then we give the explicit result for the Hawking temperature of the Kerr-Newman-AdS black hole from the tunneling approach.
We apply the counterterm subtraction technique to calculate the action and other quantities for the Kerr--AdS black hole in five dimensions using two boundary metrics; the Einstein universe and rotating Einstein universe with arbitrary angular velocity. In both cases, the resulting thermodynamic quantities satisfy the first law of thermodynamics. We point out that the reason for the violation of the first law in previous calculations is that the rotating Einstein universe, used as a boundary metric, was rotating with an angular velocity that depends on the black hole rotation parameter. Using …
