In this note we investigate the generalized massive gravity in asymptotically $AdS_3$ spacetime by combining the two mass terms of topological massive gravity and new massive gravity theory. We study the linearized excitations around the $AdS_3$ background and find that at a specific value of a certain combination of the two mass parameters (chiral line), one of the massive graviton solutions becomes the left moving massless mode. It is shown that the theory is chiral at this line under Brown-Henneaux boundary condition. Because of this degeneration of the gravitons the new log solution which has a logarithmic asymptotic behavior is also a solution to this gravity theory at the chiral line. The log boundary condition which was proposed to accommodate this log solution is proved to be consistent at this chiral line. The resulting theory is no longer chiral except at a special point on the chiral line, where another new solution with log-square asymptotic behavior exists. At this special point, we prove that a new kind of boundary condition called log-square boundary condition, which accommodates this new solution, can be consistent.
Massive arbitrary spin fields in AdS(3) spacetime are discussed in a framework of light-cone gauge formulation. We also consider compactification of AdS spacetime on manifold which is warped product of AdS space and sphere. Mass spectra of massless and massive fields upon such compactification are found.
We consider the curvatures 2 form asociated with AdSL4 valued one-form gauge connetion, and then we construct a four-dimensional action that generalize the Einstein-Hilbert gravity. It is shown that the Maxwell extension of Einstein gravity can be obtained from AdSL4-gravity making use of the Inonu-Wigner contraction method. In the same way, by gauging the AdSL5 spacetime algebra, the Einstein-Hilbert gravity is extended including the vector fields kab and ha which are associated with non-Abelian tensors and non Abelian vectors charges in the AdSL5 algebra. The B5 extension of Einstein gravity…
We calculate the holographic conformal anomaly and brane Newton potential when bulk is 5d AdS BH. It is shown that such anomaly is the same as in the case of pure AdS or (asymptotically) dS bulk spaces, i.e. it is (bulk) metric independent one. While Newton potential on the static brane in AdS BH is different from the one in pure AdS space, the gravity trapping still occurs for two branes system. This indicates to metric independence of gravity localization.
We study AdS_2 quantum gravity with emphasis on consistency with results from AdS_3. We lift AdS_2 black holes to three dimensions and map fluctuations around the solutions. Comparison with near extremal BTZ are discussed, with due emphasis on global aspects. The results confirm that parameters like central charges and conformal weights computed directly in 2D are consistent with standard results in 3D. Applying our results to the thermodynamics of near extreme Kerr black holes, we show that AdS_2 quantum gravity gives the correct central charge c=12J, and the entropy of excitations above the …
We study 2D Maxwell-dilaton gravity on AdS(2). We distinguish two distinctive cases depending on whether the AdS(2) solution can be lifted to an AdS(3) geometry. In both cases, in order to get a consistent boundary condition we need to work with a twisted energy momentum tensor which has non-zero central charge. With this central charge and the explicit form of the twisted Virasoro generators we compute the entropy of the system using the Cardy formula. The entropy is found to be the same as that obtained from gravity calculations for a specific value of the level of the U(1) current. The agre…
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 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 solutio…
We review the status of three-dimensional "general massive gravity" (GMG) in its linearization about an anti-de Sitter (adS) vacuum, focusing on critical points in parameter space that yield generalizations of "chiral gravity". We then show how these results extend to N=1 super-GMG, expanded about a supersymmetric adS vacuum, and also to the most general `curvature-squared' N=1 supergravity model.
In this note we study the properties of linearized gravitational excitations in the new massive gravity theory in asymptotically $AdS_3$ spacetime and find that there is also a critical point for the mass parameter at which massive gravitons become massless as in topological massive gravity in $AdS_3$. However, at this critical point in the new massive gravity the energy of all branches of highest weight gravitons vanish and the central charges also vanish within the Brown-Henneaux boundary conditions. The new massive gravity in asymptotically $AdS_3$ spacetime seems to be trivial at this crit…
We introduce the Einstein-Yang-Mills AdS black brane solution in context of massive gravity. The ratio of shear viscosity to entropy density is calculated for this solution. This value violates the KSS bound if we apply the Dirichlet boundary and regularity on the horizon conditions.
We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the $AdS$ background in even number of dimensions using the group theoretic approach introduced in \cite{Gopakumar:2011qs} and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost and two modes that contain mass.
In this paper, the Einstein AdS black brane solution in the presence of quintessence in context of massive gravity is introduced. The ratio of shear viscosity to entropy density for this solution violates the KSS bound by applying the Dirichlet boundary and regularity on the horizon conditions. Our result shows that this value is independent of quintessence in arbitrary dimensions.
Two-dimensional Maxwell-dilaton quantum gravity on AdS_2 with radius $\ell$ and a constant electric field E is studied. In conformal gauge, this is equivalent to a CFT on a strip. In order to maintain consistent boundary conditions, the usual conformal diffeomorphisms must be accompanied by a certain U(1) gauge transformation. The resulting conformal transformations are generated by a twisted stress tensor, which has a central charge $c={3k E^2 \ell^4/4}$ where k is the level of the U(1) current. This is an AdS_2 analog of the Brown-Henneaux formula $c = 3\ell/2G$ for the central charge of qua…
We shortly review the bi-local, collective dipole mechanism to a construction of Higher Spin AdS Gravity from the O(N) vector field theory. We also make some comments regarding an exact nonlinear comparison and in this regard we present a bi-local (symmetric) gauge description of Vasiliev's theory.
In this paper, we introduced the black brane solution in Rastall theory and in the context of massive gravity. The ratio of shear viscosity to entropy density is calculated for this solution. Our result shows that the KSS bound violates for this theory.
We obtain a closed form expression for the Action describing pure gravity, in light-cone gauge, in a four-dimensional Anti de Sitter background. We perform a perturbative expansion of this closed form result to extract the cubic interaction vertex in this gauge.
The two-point Green function of a local operator in CFT corresponding to a massive symmetric tensor field on the AdS background is computed in the framework of the AdS/CFT correspondence. The obtained two-point function is shown to coincide with the two-point function of the graviton in the limit when the mass vanishes.
We discuss dilatonic gravity (bulk theory) from the point of view of (generalized) AdS/CFT correspondence. Self-consistent dilatonic background is considered. It may be understood as two boundaries space where AdS boundary appears as infinite boundary and new (singular) boundary occurs at short distances. The two-point correlation function and conformal dimension for minimal and dilaton coupled scalar are found. Even for minimal scalar, the conformal dimension is found to be different on above two boundaries. Hence, new CFT appears in AdS/CFT correspondence at short distances. AdS/CFT correspo…
Gravity in d dimensions is formulated as the gauge theory of local SO(2,d-1) gauge group. The Chern-Pontryagin index ${\cal P}_{2n}$ plays a crucial role in both gravity and gauge theories. ${\cal P}_{2n}(gravity)$ gives the gravitational Lagrangian in 2n dimensions, having the vacuum solution $AdS_{2n}$. The same but global symmetry is shared with the gauge theories and 0,1-cochains of the Chern-Simon index ${\cal C}_{2n}(gauge)$ take part of $CFT_{2n-1}$ and $CFT_{2n-2}$, respectively. Gravity in odd dimensions is quite analogously formulated to that in even dimensions. This gives new insigh…
We explicitly calculate the induced gravity theory at the boundary of an asymptotically Anti-de Sitter five dimensional Einstein gravity. We also display the action that encodes the dynamics of radial diffeomorphisms. It is found that the induced theory is a four dimensional conformal gravity plus a scalar field. This calculation confirms some previous results found by a different approach.
I review some interesting features of massive gravity in two maximally symmetric backgrounds: Anti de Sitter space and Minkowski space. While massive gravity in AdS can be seen as a spontaneously broken, UV safe theory, no such interpretation exists yet in the flat-space case. Here, I point out the problems encountered in trying to find such completion, and possible mechanisms to overcome them.
We formulate a first quantized construction of the AdS_{d+1}/CFT_d correspondence using the bi-local representation of the free d-dimensional large N vector model. The earlier reconstruction of AdS_4 higher-spin gravity provides a scheme where the AdS spacetime (and higher-spin fields) are given by the composite bi-local fields. The underlying first quantized, world-sheet picture is extracted in the present work and generalized to any dimension. A higher-spin AdS particle model is shown to emerge from the collective bi-particle system of Minkowski particles through a canonical transformation. …
We introduce a new Lie bialgebra structure for the anti de Sitter (AdS) Lie algebra in (2+1)-dimensional spacetime. By gauging the resulting \textit{AdS Lie bialgebra}, we write a Chern-Simons gauge theory of bi-gravity involving two dreibeins rather than two metrics, which describes two interacting massless spin-2 fields. Our ghost-free bi-gravity model which has no any local degrees of freedom, has also a suitable free field limit. By solving its equations of motion, we obtain a \textit{new black hole} solution which has two curvature singularities and two horizons. We also study cosmologica…
Higher derivative bulk gravity (without Riemann tensor square term) admits AdS-Schwarzschild black hole as exact solution. It is shown that induced brane geometry on such background is open, flat or closed FRW radiation dominated Universe. Higher derivative terms contributions appear in the Hawking temperature, entropy and Hubble parameter via the redefinition of 5-dimensional gravitational constant and AdS scale parameter. These higher derivative terms do not destroy the AdS-dual description of radiation represented by strongly-coupled CFT. Cardy-Verlinde formula which expresses cosmological …
Two-dimensional BF theory with infinitely many higher spin fields is proposed. It is interpreted as the AdS(2) higher spin gravity model describing a consistent interaction between local fields in AdS(2) space including gravitational field, higher spin partially-massless fields, and dilaton fields. We carry out analysis of the frame-like and the metric-like formulation of the theory. Infinite-dimensional higher spin global algebras and their finite-dimensional truncations are realized in terms of o(2,1) - sp(2) Howe dual auxiliary variables.
We consider asymptotically Warped AdS$_3$ black holes in Topologically Massive Gravity. We study their thermodynamic stability and show the existence of a Hawking-Page phase transition between the black hole and thermal background phases. At zero angular potential, the latter is shown to occur at the self-dual point of the dual Warped Conformal Field Theory partition function, in analogy with the phase transition for BTZ black holes in AdS$_3$/CFT$_2$. We also discuss how the central and vacuum charges can be obtained from inner horizon mechanics in the presence of a gravitational anomaly.
Stability of dilatonic AdS spaces due to quantum effects of dilaton coupled conformal matter is considered. When such spaces do not exist on classical level, their dynamical generation occurs. Explicit examples corresponding to quantum creation of d4 dilatonic AdS Universe and of d2 dilatonic AdS Black Hole (BH) are presented. Motivated by holographic RG, in the similar approach the complete d5 effective action is discussed. The intermediate region where it is the sum of two parts: bulk (classical gravity) and boundary quantum action is investigated. The effective equations solution representi…
Motivated by the AdS_6/CFT_5 correspondence, we study general supersymmetric solutions of massive type IIA supergravity, consisting of a warped product of six-dimensional anti-de Sitter space AdS_6 with a four-dimensional Riemannian manifold M_4, and fluxes compatible with the SO(5,2) symmetry. We find that the only local solution of this form is the warped AdS_6 x_w S^4 solution, originally discovered by Brandhuber and Oz. We discuss the supersymmetric properties of this solution.
AdS3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point μl=1. We study the possibility that the warped vacua of TMG, which exist for all values of μ, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS3 vacua with Compere-Detournay boundary conditions are indeed stable in the range μl > 3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS3 vacuum. The situation somewhat resembles chiral gravit…
We study massless and massive Hawking radiations on a two-dimensional AdS spacetime. For the massless case, the quantum stress-energy tensor of a massless scalar field on the AdS background is calculated, and the expected null radiation is obtained. However, for the massive case, the scattering analysis is performed in order to calculate the absorption and reflection coefficients which are related to statistical Hawking temperature. On the contrary to the massless case, we obtain a nonvanishing massive radiation.
We show that the parameter space of Zwei-Dreibein Gravity (ZDG) in AdS3 exhibits critical points, where massive graviton modes coincide with pure gauge modes and new `logarithmic' modes appear, similar to what happens in New Massive Gravity. The existence of critical points is shown both at the linearized level, as well as by finding AdS wave solutions of the full non-linear theory, that behave as logarithmic modes towards the AdS boundary. In order to find these solutions explicitly, we give a reformulation of ZDG in terms of a single Dreibein, that involves an infinite number of derivatives.…
We address the localization of gravity on the Friedmann-Robertson-Walker type brane embedded in either $AdS_{5}$ or $dS_{5}$ bulk space,and derive two definite limits between which the value of the bulk cosmological constant has to lie in order to localize the graviton on the brane.The lower limit implies that the brane should be either $dS_{4}$ or 4d Minkowski in the $AdS_{5}$ bulk.The positive upper limit indicates that the gravity can be trapped also on curved brane in the $dS_{5}$ bulk space.Some implications to recent cosmological scenarios are also discussed.
The renormalization group flow of the worldvolume theory depends very much from the number of unbroken supersymmetries. In the dual $AdS$ picture we break supersymmetry by adding different types of BPS black holes. We argue, that this BPS black hole causes a non-trivial renormalization group flow in the worldvolume field theory and especially a regular horizon translates into a non-trivial IR fixpoint. For this interpretation we have to rewrite the $AdS$ models into a flat space description with a linear dilaton vacuum. The dual models (linear dilaton and the $AdS$ vacuum) can be seen as the d…
Quantum gravity (QG) on two-dimensional anti-de Sitter spacetime (AdS_2) takes always the form of a chiral conformal field theory (CFT). However, the actual content of the CFT, and in particular its central charge, depends on the background values of the dilaton and Maxwell field. We review the main features of AdS_2 QG with linear dilaton and of AdS_2 QG with constant dilaton and Maxwell field. We also show that the 3D charged Banados-Teitelboim-Zanelli black hole interpolates between these two versions of AdS_2 QG. Applications to the computation of the microscopic entropy of black holes are…
We study a bi-parametric family of dilaton gravity models with constant and negative curvature. This family includes the Jackiw-Teitelboim gravity and the Liouville gravity model induced by a bosonic string. Furthermore, this family is conformally equivalent to the hiperbolic dilaton models. We propose boundary conditions in the Fefferman-Graham and in the Eddington-Finkelstein gauge. We check the consistency of the asymptotic conditions by computing the entropy of their black hole solution.
We calculate small correction terms to gravitational potential on Randall-Sundrum brane with an induced Einstein term. The behaviors of the correction terms depend on the magnitudes of $AdS$ radius $k^{-1}$ and a characteristic length scale $ł$ of model. We represent the gravitational potential for arbitrary $k$ and $ł$ at all distances.
The coexistence curve and molecule number density of a 4-dimensional AdS topological charged black hole in massive gravity is investigated. We find that the analytic expression of the coexistence curve in the reduced parameter space is dependent on theory parameters. This is very different from the previous results obtained in other modified gravity such as $f(R)$ gravity and Gauss-Bonnet gravity. Besides, we derive the explicit expression of the physical quantity which describes the difference of the number densities of AdS topological charged black hole molecules between the small and large …
We calculate the expectation value of the Wilson line in the pure AdS$_3$ Einstein gravity theory and also the entanglement entropy in the boundary theory. Our one-loop calculation of entanglement entropy shows a shift of the central charge 26. Finally, we show that the Wilson line provides the equivalent description to the boundary entanglement entropy. This equivalence leads to a concrete example of the building of "minimum surface=entanglement entropy".
Using Poincare parametrization of AdS space, we study massive totally symmetric arbitrary spin fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized by using Stueckelberg formulation of massive fields. We demonstrate that the mass parameter, curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS massive fields can be expressed in terms of ladder operators. Three representations for the Lagrangian are discussed. Realization of the global AdS …
We show the universal form of the boundary term (Kounterterm series) which regularizes the Euclidean action and background-independent definition of conserved quantities for any Lovelock gravity theory with AdS asymptotics (including Einstein-Hilbert and Einstein-Gauss-Bonnet). We discuss on the connection of this procedure to the existence of topological invariants and Chern-Simons forms in the corresponding dimensions.
We determine the Killing spinors for a class of magnetic brane solutions with Minkowski worldvolume of the theory of AdS Einstein Maxwell theories in d dimensions. We also obtain curved magnetic brane solutions with Ricci-flat worldvolumes. If we demand that the curved brane solution admits Killing spinors, then its worldvolume must admit parallel spinors. Classes of Ricci-flat worldvolumes admitting parallel spinors are discussed.
We construct the frame-like gauge-invariant Lagrangian formulation for massive fermionic arbitrary spin fields in three-dimensional $AdS$ space. The Lagrangian and complete set of gauge transformations are obtained. We also develop the formalism of gauge-invariant curvatures for the massive theory under consideration and show how the Lagrangian is formulated in their terms. The massive spin-5/2 field is discussed as an example.
In this paper, we use the Karch-Randall braneworld to study theories of quantum gravity in two dimensional (nearly) anti-de Sitter space (AdS$_2$). We focus on effective gravitational theories in the setup with two Karch-Randall branes embedded in an asymptotically AdS$_3$ bulk forming a wedge. We find the appearance of two-dimensional Einstein-Hilbert gravity (or the Lorenzian version of Marolf-Maxfield theory) when the branes are rigid but the emergence of a class of dilaton gravity models parameterized by the tensions of the two branes when brane fluctuations are accounted for. A special ca…
Free totally symmetric arbitrary spin massive bosonic and fermionic fields propagating in AdS(d) are investigated. Using the light cone formulation of relativistic dynamics we study bosonic and fermionic fields on an equal footing. Light-cone gauge actions for such fields are constructed. Interrelation between the lowest eigenvalue of the energy operator and standard mass parameter for arbitrary type of symmetry massive field is derived.
Verlinde argued \cite{Verlinde:2016toy} that baryonic matter in de Sitter Universe with a Hubble constant $H$ produces a bulk contribution to the vacuum entanglement entropy $δS_{ent}$. Using the de Sitter temperature $T_{dS}=\frac{H}{2π}$, he interpreted $δM$ in the first law $T_{dS}\ δS_{ent}=-δM$ with the Dark Matter energy. We use standard tools of the gauge/gravity correspondence to present some evidence for the Verlinde's proposal.
One of explanations of the black hole entropy implies that gravity is entirely induced by quantum effects. By using arguments based on the AdS/CFT correspondence we give induced gravity interpretation of the gravity in a brane world in higher dimensional anti-de Sitter (AdS) space. The underlying quantum theory is SU(N) theory where $N$ is related to the CFT central charge. The theory includes massless fields which correspond to degrees of freedom of the boundary CFT. In addition, on the brane there are massive degrees of freedom with masses proportional to $l^{-1}$ where $l$ is the radius of …
By considering the fifth order term of the interaction potential in massive gravity theory, we study the $P-V$ critical behaviors of AdS black hole in $d \geq 7$ dimensional space-time, and find the tricritical point and the solid/liquid/gas phase transition in addition to the Van der Waals-like phase and the reentrant phase transition of the system. The critical phenomena of black holes depend crucially on the number $n$ of interaction potential terms.
We investigate the AdS/CFT correspondence for higher-derivative gravity systems, and develop a formalism in which the generating functional of the boundary field theory is given as a functional that depends only on the boundary values of bulk fields. We also derive a Hamilton-Jacobi-like equation that uniquely determines the generating functional, and give an algorithm calculating the Weyl anomaly. Using the expected duality between a higher-derivative gravity system and N=2 superconformal field theory in four dimensions, we demonstrate that the resulting Weyl anomaly is consistent with the fi…
We construct in this paper a multi-brne model with Minkowski and AdS spacetime alternated in the fifth dimension and study the gravity on the brane of our universe. We will show that in this model there are both the graviton-like resonant states which generates the "quasi-localized gravity" and the resonant states of the massive KK mode. This model gives rise to gravity which deviates from the Newton gravitational potential at small and large scale which, however can be shown to be consistent with the observations in the absence of fine-tuning of the model parameters.
We explore the connection between anti-deSitter supergravity and gauge theory, in the context of bound states of many D1 and D5 branes. The near-horizon $AdS_3$ supergravity describes the identity sector of the conformal field theory produced by the brane dynamics. A variant of anomaly inflow (for the 2d conformal anomaly) is involved. Dynamical matter fields on $AdS_3$ couple to the chiral ring and its descendant fields on the branes. We propose a map between boundary conformal field theory and bulk supergravity/matter dynamics, which is strongly reminiscent of matrix models of 2d gravity.
We study the localization of gravity on string-like defects in codimension two. We point out that the gravity-localizing `local cosmic string' spacetime has an orbifold singularity at the horizon. The supergravity embedding and the AdS/CFT correspondence suggest ways to resolve the singularity. We find two resolutions of the singularity that have a semiclassical gravity description and study their effect on the low-energy physics on the defect. The first resolution leads, at long distances, to a codimension one Randall-Sundrum scenario. In the second case, the infrared physics is like that of …
Naively applying holographic duality to gapped gravity on Anti de Sitter (AdS) space seems to suggest that the stress tensor of the field theory dual cannot be conserved. On the other hand, by symmetry arguments, it seems that the dual should not violate Poincare symmetry. To clarify this apparent contradiction, we study a holographic dual of massive gravity where both the physical background metric and the fiducial metric are AdS. Using the anomalous scaling of the energy momentum tensor as our guide, we conclude that the dual theory is nonlocal. We find that the dual is similar to conformal …
A proposal to describe gravity duals of conformal theories with boundaries (AdS/BCFT correspondence) was put forward by Takayanagi few years ago. However interesting solutions describing field theories at finite temperature and charge density are still lacking. In this paper we describe a class of theories with boundary, which admit black hole type gravity solutions. The theories are specified by stress-energy tensors that reside on the extensions of the boundary to the bulk. From this perspective AdS/BCFT appears analogous to the fluid/gravity correspondence. Among the class of the boundary e…
We discuss some properties of higher derivative (HD) bulk gravity without Riemann tensor square term. Such a kind of gravity admits Schwarzschild Anti de Sitter (SAdS) black hole as exact solution. It is shown that induced brane geometry on such background is Friedmann-Robertson-Walker (FRW) radiation dominated Universe. We show that HD terms contributions appear in the Hawking temperature, entropy and Hubble parameter via the redefinition of 5-dimensional gravitational constant and AdS scale parameter. These HD terms do not destroy the AdS-dual description of radiation represented by strongly…
A higher dimensional gravity invariant both under local Lorentz rotations and under local Anti de Sitter boosts is constructed. It is shown that such a construction is possible both when odd dimensions and when even dimensions are considered. It is also proved that such actions have the same coefficients as those obtained by Troncoso and Zanelli.
The boundary charges which constitute the Virasoro algebra in 2+1 dimensional anti-de Sitter gravity are derived by way of Noether theorem and diffeomorphic invariance. It shows that the boundary charges under discussion recently exhaust all the independent nontrivial charges available. Therefore, the state counting via the Virasoro algebra is complete.
Free mixed-symmetry arbitrary spin massive bosonic and fermionic fields propagating in AdS(5) are investigated. Using the light-cone formulation of relativistic dynamics we study bosonic and fermionic fields on an equal footing. Light-cone gauge actions for such fields are constructed. Various limits of the actions are discussed.
We calculate 2-point correlators for New Massive Gravity at the chiral point and find that they behave precisely as those of a logarithmic conformal field theory, which is characterized in addition to the central charges c_L = c_R = 0 by `new anomalies' b_L = b_R = -σ\frac{12\ell}{G_N}, where σis the sign of the Einstein-Hilbert term, \ell the AdS radius and G_N Newton's constant.
