Dual Conformal Field Theory Research Articles

Simulation of asymptoticallyAdS5spacetimes with a generalized harmonic evolution scheme

Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter spacetimes. We work in global ${\mathrm{AdS}}_{5}$, which can be described by the ($t$, $r$, $\ensuremath{\chi}$, $\ensuremath{\theta}$, $\ensuremath{\phi}$) spherical coordinates adapted to the $\mathbb{R}\ifmmode\times\else\texttimes\fi{}{S}^{3}$ boundary. We focus on solutions that preserve an $SO(3)$ symmetry that acts to rotate the 2-spheres parametrized by $\ensuremath{\theta}$, $\ensuremath{\phi}$. In the boundary conformal field theory, the way in which this symmetry manifests itself hinges on the way we choose to embed Minkowski space in $\mathbb{R}\ifmmode\times\else\texttimes\fi{}{S}^{3}$. We present results from an ongoing study of prompt black hole formation via scalar field collapse, and explore the subsequent quasinormal ringdown. Beginning with initial data characterized by highly distorted apparent horizon geometries, the metrics quickly evolve, via quasinormal ringdown, to equilibrium static black hole solutions at late times. The lowest angular number quasinormal modes are consistent with the linear modes previously found in perturbative studies, whereas the higher angular modes are a combination of linear modes and of harmonics arising from nonlinear mode coupling. We extract the stress energy tensor of the dual conformal field theory on the boundary, and find that despite being highly inhomogeneous initially, it nevertheless evolves from the outset in a manner that is consistent with a thermalized $\mathcal{N}=4\text{ }\text{ }\mathrm{SYM}$ fluid. As a first step towards closer contact with relativistic heavy ion collision physics, we map this solution to a Minkowski piece of the $\mathbb{R}\ifmmode\times\else\texttimes\fi{}{S}^{3}$ boundary, and obtain a corresponding fluid flow in Minkowski space.

Higher spin quasinormal modes and one-loop determinants in the BTZ black hole

We solve the wave equations of arbitrary integer spin fields in the BTZ black hole background and obtain exact expressions for their quasinormal modes. We show that these quasinormal modes precisely agree with the location of the poles of the corresponding two point function in the dual conformal field theory as predicted by the AdS/CFT correspondence. We then use these quasinormal modes to construct the one-loop determinant of the higher spin field in the thermal BTZ background. This is shown to agree with that obtained from the corresponding heat kernel constructed recently by group theoretic methods.

Holographic horizons

We examine how the $(2+1)$-dimensional anti-de Sitter space is covered by the Fefferman-Graham system of coordinates for Minkowski, Rindler, and static de Sitter boundary metrics. We show that, in the last two cases, the coordinates do not cover the full anti-de Sitter space. On a constant-time slice, the line delimiting the excluded region has endpoints at the locations of the horizons of the boundary metric. Its length, after an appropriate regularization, reproduces the entropy of the dual conformal field theory on the boundary background. The horizon can be interpreted as the holographic image of the line segment delimiting the excluded region in the vicinity of the boundary.

Higher spin AdS3 supergravity and its dual CFT

Vasiliev's higher spin supergravity theory on three dimensional anti-de Sitter space is studied and, in particular, the partition function is computed at one loop level. The dual conformal field theory is proposed to be the N=(2,2) CP^N Kazama-Suzuki model in two dimensions. The proposal is based on symmetry considerations and comparison of the bulk partition function with the conformal field theory. Our findings suggest that the theory is strong-weak self-dual.

Noncritical Einstein-Weyl gravity and the AdS/CFT correspondence

We explore four-dimensional Einstein-Weyl gravity and supergravity on anti-de Sitter spacetime. For a specific range of the coupling with appropriate boundary conditions, we show the effective equivalence of the theory with Einstein gravity and AdS supergravity at the quadratic Lagrangian level. Furthermore we show that these equivalences can be promoted to the full nonlinear level. We also show that the similar behavior holds for the generalized Gibbons-Hawking terms. From this we find that the correlation functions in the dual conformal field theory of Einstein-Weyl gravity and supergravity can be readily read off from corresponding ones from Einstein gravity and AdS supergravity. We also give comments on some issues in critical gravity and supergravity as well as conformal gravity and supergravity.

Statistical entropies of extremal Kaluza-Klein AdS black holes in arbitrary dimensions

We have investigated the microscopic interpretations of the entropies for the four-dimensional extremal Kaluza-Klein AdS black hole and its higher-dimensional generalizations by using the Kerr/CFT correspondence. These newly-found Kaluza-Klein AdS black holes are charged rotating asymptotically AdS black hole solutions of gauged supergravity in four and higher dimensions. With suitable boundary conditions on the perturbations of the near-horizon geometry, it is shown that the asymptotic symmetry generators form a two-dimensional Virasoro algebra with a central term. By utilizing the central charge and the temperature of the dual conformal field theory, Cardy formula reproduces the expected Bekenstein-Hawking entropy. Directly working on the ordinary metrics of the extremal Kaluza-klein AdS black holes without taking the near-horizon limit, we also re-derive their microscopic entropies.

The BTZ black hole with a time-dependent boundary

The non-rotating BTZ solution is expressed in terms of coordinates that allow for an arbitrary time-dependent scale factor in the boundary metric. We provide explicit expressions for the coordinate transformation that generates this form of the metric, and determine the regions of the complete Penrose diagram that are covered by our parametrization. This construction is utilized in order to compute the stress–energy tensor of the dual conformal field theory (CFT) on a time-dependent background. We study in detail the expansion of radial null geodesic congruences in the BTZ background, for various forms of the scale factor of the boundary metric. We also discuss the relevance of our construction for the holographic calculation of the entanglement entropy of the dual CFT on time-dependent backgrounds.

Flows to Schrödinger geometries

We construct renormalization group flow solutions interpolating anti-de Sitter and Schr\"odinger geometries in Abelian Higgs models obtained from consistent reductions of type IIB supergravity and M theory. We find that $z=2$ Schr\"odinger geometries can be realized at the minima of scalar potentials of these models, where a scalar charged under $U(1)$ gauge symmetry obtains a nonzero vacuum expectation value. The renormalization group flows are induced by an operator deformation of the dual conformal field theory. The flows are captured by fake superpotentials of the theories.

Flowing between fermionic fixed points

We study holographic Wilsonian renormalization group flows for bulk spinor fields in AdS. We use this to compute the all-loop beta function for fermionic double trace operators in the dual conformal field theory.

Chronology protection in stationary 3D spacetimes

We study chronology protection in stationary, rotationally symmetric space-times in 2 + 1 dimensional gravity, focusing especially on the case of negative cosmological constant. We show that in such spacetimes closed timelike curves must either exist all the way to the boundary or, alternatively, the matter stress tensor must violate the null energy condition in the bulk. We also show that the matter in the closed timelike curve region gives a negative contribution to the conformal weight from the point of view of the dual conformal field theory. We illustrate these properties in a class of examples involving rotating dust in antide Sitter space, and comment on the use of the AdS/CFT correspondence to study chronology protection.

Correspondence between the contracted BTZ solution of cosmological topological massive gravity and two-dimensional Galilean conformal algebra

We show that a BTZ black hole solution of cosmological topological massive gravity has a hidden conformal symmetry. In this regard, we consider the wave equation of a massless scalar field propagating in BTZ spacetime and find that the wave equation could be written in terms of the SL(2, R) quadratic Casimir. From the conformal coordinates, the temperatures of the dual conformal field theories (CFTs) could be read directly. Moreover, we compute the microscopic entropy of the dual CFT by the Cardy formula and find a perfect match to the Bekenstein–Hawking entropy of a BTZ black hole. Then, we consider Galilean conformal algebras (GCA), which arises as a contraction of relativistic conformal algebras (x → ϵx, t → t, ϵ → 0). We show that there is a correspondence between GCA2 on the boundary and contracted BTZ in the bulk. For this purpose we obtain the central charges and temperatures of GCA2. Then, we compute the microscopic entropy of the GCA2 by the Cardy formula and find a perfect match to the Bekenstein–Hawking entropy of a BTZ black hole in a non-relativistic limit. The absorption cross section of a near-region scalar field also matches the microscopic absorption cross section of the dual GCA2. So we find further evidence that shows correspondence between a contracted BTZ black hole and two-dimensional GCA.

Holograms of conformal Chern-Simons gravity

We show that conformal Chern-Simons gravity in three dimensions has various holographic descriptions. They depend on the boundary conditions on the conformal equivalence class and the Weyl factor, even when the former is restricted to asymptotic Anti-deSitter behavior. For constant or fixed Weyl factor our results agree with a suitable scaling limit of topologically massive gravity results. For varying Weyl factor we find an enhancement of the asymptotic symmetry group, the details of which depend on certain choices. We focus on a particular example where an affine u(1) algebra related to holomorphic Weyl rescalings shifts one of the central charges by 1. The Weyl factor then behaves as a free chiral boson in the dual conformal field theory.

Near-horizon limits of massless BTZ and their CFT duals

We consider the massless Bañados–Teitelboim–Zanelli (BTZ) black hole and show that it is possible to take its ‘near-horizon’ limit in two distinct ways. The first one leads to a null self-dual orbifold of AdS3 and the second to a singular spacelike AdS orbifold in the large K limit, the ‘pinching orbifold’. We show that from the dual 2D conformal field theory (CFT) viewpoint, the null orbifold corresponds to the p+ = 0 sector of the discrete light-cone quantization of the 2D CFT where a chiral sector of the CFT is decoupled, while the pinching orbifold corresponds to taking an infinite mass gap limit on both the right and left sectors of the 2D CFT, essentially leaving us with the states only. In the latter case, one can combine the near-horizon limit with sending the 3D Planck length ℓP to zero or equivalently the dual 2D CFT central charge c to infinity. We provide preliminary evidence that in the latter case some nontrivial dynamics may survive the limit.

Twofold hidden conformal symmetries of rotating charged Gödel black holes

In this paper, we show that there are two different individual 2D conformal field theories (CFTs) holographically dual to the rotating charged Gödel black hole. First, we consider the J-picture descriptions. For the charged rotating black holes in the five-dimensional Gödel universe, the J-picture descriptions are associated with two angular momenta. Then, we explore the supplementary holographic description, the Q-picture, based on the electric charge of the black hole. We consider the wave equation of a massless charged scalar field in our interesting background and show in the ‘near-horizon region’ that the wave equation can be reproduced by the SL(2, R)L × SL(2, R)R Casimir quadratic operators. Moreover, we compute the microscopic entropy of the dual CFT by the Cardy formula and find a perfect match to the Bekenstein–Hawking entropy of Kerr charged Gödel spacetimes. The absorption cross section of a near-region scalar field also matches the microscopic absorption cross section of the dual CFT.

Vacua of N = 10 three-dimensional gauged supergravity

We study scalar potentials and the corresponding vacua of N = 10 three-dimensional gauged supergravity. The theory contains 32 scalar fields parametrizing the exceptional coset space . The admissible gauge groups considered in this work involve both compact and non-compact gauge groups which are maximal subgroups of SO(10) × U(1) and E6( − 14), respectively. These gauge groups are given by SO(p) × SO(10 − p) × U(1) for p = 6, …, 10, SO(5) × SO(5), SU(4, 2) × SU(2), G2( − 14) × SU(2, 1) and F4( − 20). We find many AdS3 critical points with various unbroken gauge symmetries. The relevant background isometries associated with the maximally supersymmetric critical points at which all scalars vanish are also given. These correspond to the superconformal symmetries of the dual conformal field theories in two dimensions.

Modes of log gravity

The physical modes of a recently proposed $D$-dimensional ``critical gravity'', linearized about its anti-de Sitter vacuum, are investigated. All ``log mode'' solutions, which we categorize as ``spin-2'' or ``Proca'', arise as limits of the massive spin-2 modes of the noncritical theory. The linearized Einstein tensor of a spin-2 log mode is itself a `nongauge' solution of the linearized Einstein equations whereas the linearized Einstein tensor of a Proca mode takes the form of a linearized general coordinate transformation. Our results suggest the existence of a holographically dual logarithmic conformal field theory.

Constructing local bulk observables in interacting AdS/CFT

Local operators in the bulk of anti-de Sitter can be represented as smeared operators in the dual conformal field theory. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. Large-$N$ factorization plays a key role in the construction. We show diagrammatically how this procedure is related to bulk Feynman diagrams.

ABJM dibaryon spectroscopy

We extend the proposal for a detailed map between wrapped D-branes in Anti-de Sitter space and baryon-like operators in the associated dual conformal field theory provided in hep-th/0202150 to the recently formulated AdS_4 \times CP^3/ABJM correspondence. In this example, the role of the dibaryon operator of the 3-dimensional CFT is played by a D4-brane wrapping a CP^2 \subset CP^3. This topologically stable D-brane in the AdS_4 \times CP^3 is nothing but one-half of the maximal giant graviton on CP^3.

MULTISPIN MEMBRANE SOLUTIONS IN AdS4 ×Q1, 1, 1

We study several types of classical rotating membrane solutions in AdS 4 ×Q1, 1, 1 and discuss their field theory duals. Q1, 1, 1 is a seven-dimensional Sasaki–Einstein manifold given as a nontrivial U(1) fibration over S2×S2×S2, equipped with SU(2)3 ×U(1) isometry. It is recently suggested that there exist quiver Chern–Simons theories which are dual to M-theory in certain orbifolds of Q1, 1, 1. The membrane solutions we consider have in general nonvanishing angular momenta both in AdS 4 and Q1, 1, 1 spaces. We present solutions for folded and wrapped membranes. According to the AdS/CFT correspondence, such classical solutions are dual to long operators of the dual conformal field theories in the large coupling limit. We analyze the asymptotic behaviour of the dispersion relation between energy (conformal dimension) and angular momenta (global charges).

AnAdS3dual for minimal model CFTs

We propose a duality between the 2d ${\mathcal{W}}_{N}$ minimal models in the large $N$ 't Hooft limit, and a family of higher spin theories on ${\mathrm{AdS}}_{3}$. The 2d conformal field theories (CFTs) can be described as Wess-Zumino-Witten coset models, and include, for $N=2$, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the renormalization group flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an ${\mathrm{AdS}}_{4}$ dual for the singlet sector of large $N$ vector models.