Dimensional Anti-de Sitter Space Research Articles

Oscillatingp-branes

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the Poincare symmetries of D dimensional space-time due to the embedding of a p-brane with codimension N=D-p-1. The resulting world volume action is an ISO(1,p+N) invariant generalization of the Nambu-Goto action in d=p+1 dimensional space-time. Analogous results are obtained for an anti-de Sitter (AdS) p-brane with codimension N embedded in D dimensional AdS space, yielding an SO(2,p+N) invariant version of the Nambu-Goto action in d=p+1 dimensional space-time. Attention is focused on a supersymmetric extension of the D=6 Minkowski space case with an embedded p=3 brane; a particular realization of which is provided by a non-BPS vortex. Here both the Nambu-Goto-Akulov-Volkov action and its dual tensor form are presented.

Quantum critical transport, duality, and M theory

We consider charge transport properties of $2+1$ dimensional conformal field theories at nonzero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For $\mathcal{N}=8$ supersymmetric, $\mathrm{SU}(N)$ Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large $N$ limit by applying the anti-de Sitter/conformal field theory (AdS/CFT) correspondence to M theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in $3+1$ dimensional anti-de Sitter space. The electromagnetic self-duality of the $3+1$ dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in $2+1$ dimensional Abelian theories. Thus the $2+1$ dimensional, superconformal Yang Mills theory obeys a ``holographic self-duality'' in the large $N$ limit, and perhaps more generally.

Phase transitions in higher derivative gravity

This paper deals with black holes, bubbles and orbifolds in Gauss-Bonnet theory in five dimensional anti de Sitter space. In particular, we study stable, unstable and metastable phases of black holes from thermodynamical perspective. By comparing bubble and orbifold geometries, we analyse associated instabilities. Assuming AdS/CFT correspondence, we discuss the effects of this higher derivative bulk coupling on a specific matrix model near the critical points of the boundary gauge theory at finite temperature. Finally, we propose another phenomenological model on the boundary which mimics various phases of the bulk space-time.

Exact gravitational quasinormal frequencies of topological black holes

We compute the exact gravitational quasinormal frequencies for massless topological black holes in $d$-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies.

Holography and renormalization in Lorentzian signature

De Boer et. al. have found an asymptotic equivalence between the Hamilton-Jacobi equations for supergravity in (d+1)-dimensional asymptotic anti-de Sitter space, and the Callan-Symanzik equations for the dual d-dimensional perturbed conformal field theory. We discuss this correspondence in Lorentzian signature. We construct a gravitational dual of the generating function of correlation functions between initial and final states, in accordance with the construction of Marolf, and find a class of states for which the result has a classical supergravity limit. We show how the data specifying the full set of solutions to the second-order supergravity equations of motion are described in the field theory, despite the first-order nature of the renormalization group equations for the running couplings: one must specify both the couplings and the states, and the latter affects the solutions to the Callan-Symanzik equations.

A new characterization of hyperbolic cylinder in anti-de Sitter space [formula omitted

By investigating n-dimensional complete maximal spacelike hypersurfaces with two distinct principal curvatures in an ( n + 1 ) -dimensional anti-de Sitter space H 1 n + 1 ( − 1 ) , we give a new characterization of hyperbolic cylinder H m ( − n m ) × H n − m ( − n n − m ) in H 1 n + 1 ( − 1 ) .

Anti-de Sitter space, squashed and stretched

We study the Lorentzian analogues of the squashed 3-sphere, namely, (2+1)-dimensional anti-de Sitter space squashed or stretched along fibres that are either spacelike or timelike. The causal structure and the property of being an Einstein–Weyl space depend critically on whether we squash or stretch. We argue that squashing and stretching completely destroy the conformal boundary of the unsquashed spacetime. As a physical application we observe that the near horizon geometry of the extremal Kerr black hole, at constant Boyer–Lindquist latitude, is anti-de Sitter space squashed along compactified spacelike fibres.

Asymptotic Behaviour of Solitons with a Double SpectralParameter for the Bogomolny Equation in (2+1)-Dimensional Anti de SitterSpace

The asymptotic behaviour of the solitons with a double spectralparameter for the Bogomolny equation in (2+1)-dimensional anti deSitter space is obtained. The asymptotic solution has two ridgesclose to each other which locates beside the geodesic of thePoincaré half-plane.

Publisher’s Note: Eternal time machine in (2+1)-dimensional anti–de Sitter space [Phys. Rev. D66, 084020 (2002)

2+1 dimensional anti-de Sitter space has been the subject of much recent investigation. Studies of the behaviour of point particles in this space have given us a greater understanding of the BTZ black hole solutions produced by topological identification of adS isometries. In this paper, we present a new configuration of two orbiting massive point particles that leads to an ``eternal'' time machine, where closed timelike curves fill the entire space. In contrast to previous solutions, this configuration has no event or chronology horizons. Another interesting feature is that there is no lower bound on the relative velocities of the point masses used to construct the time machine; as long as the particles exceed a certain mass threshold, an eternal time machine will be produced.

Relation between the solitons of Yang–Mills–Higgs fields in 2+1 dimensional Minkowski space–time and anti-de Sitter space–time

The Yang–Mills–Higgs–Bogomolny equations in both 2+1 dimensional Minkowski space–time and 2+1 dimensional anti-de Sitter space–time are known to be integrable and their soliton solutions have already been obtained. In this article, we show that there is a natural relation between the Lax pairs and soliton solutions in these two space–times when the curvature changes from 0 to −1. The changes of the asymptotic behaviors of the solitons are also discussed.

Fermion vacuum energies in brane world models

The fermion representations and boundary conditions in five dimensional anti de Sitter space are described in detail. In each case the one loop effective action is calculated for massless fermions. The possibility of topological or Wilson loop symmetry breaking is discussed.

Spinor exchange in AdS d+1

We explicitly calculate a Witten diagram with general spinor field exchange on ( d+1)-dimensional Euclidean Anti-de Sitter space, which is necessary to evaluate four-point correlation functions with spinor fields when we make use of the AdS/CFT correspondence, especially in supersymmetric cases. We also show that the amplitude can be reduced to a scalar exchange amplitude. We discuss the operator product expansion of the dual conformal field theory by interpreting the short distance expansion of the amplitude according to the AdS/CFT correspondence.

Semiclassical limit for the Binegar–Zierau quantization of the minimal nilpotent orbits of SOo(2p,2)

Let n be an odd integer greater than 3 and X be the (n+1)-dimensional anti-de Sitter space–time. Binegar and Zierau have constructed in Commun. Math. Phys. 138, 245–258 (1991) a unitary representation H=H+⊕H− of the conformal group SOo(n+1,2) of X. They have shown that this particular representation is, in a certain algebraic sense, a quantization of the union, On+1min=On+1min+∪On+1min−, of the two minimal nilpotent orbits in so(n+1,2) [Commun. Math. Phys. 138, 245–258 (1991)]. (This work is part of the author’s Ph.D. thesis.) In spite of this, it is known how to obtain ℋ from On+1min using a known quantization procedure. One reason for this interest in ℋ is that, in the case n=3, H+ is the representation carried by the one-particle sector of the massless scalar field on the anti-de Sitter space–time X. In this paper, we strengthen this link between the coadjoint orbits On+1min± and H±, by studying the semiclassical limit of the latter. In this way, we clarify their appearance in the massless theory and corroborate the existing evidence that H± is the “correct” quantization of On+1min±. As a preliminary, we show that the projection onto so(n,2)* of On+1min± is the union of the two coadjoint orbits Ono± and Onmin± (Proposition IV.1); one of those is the phase space of the classical massless particle on X. We then show (Theorem VI.1 and Corollary VI.3) that the semiclassical limit of the spectral counting function of the generator of the SO(2) subgroup of SOo(n,2) in the representation H± is dominated by a Weyl term, expressed naturally in terms of the symplectic volume of a compact portion of the classical phase space Ono±. Furthermore, we show (Theorem VI.4) that the highest weight vectors of the representation coincide in the semiclassical limit with the BKW functions constructed starting from Ono±. We show in addition that, even though the orbit method applied to On+1min± does not yield H±, it nevertheless establishes a natural relation between them. Namely, the simple SO(n+1)×S0(2)-modules appearing in H+ are those we obtain if we apply the orbit method to integral SO(n+1)×S0(2)-orbits contained in the projection on (so(n+1)⊕so(2))* of On+1min± (Sec. VII). As a by-product of our analysis, we study the restriction to SOo(n,2) of ℋ (Proposition VIII.1) and we show that the unitary structure on ℋ is exactly a Klein–Gordon scalar product on X (Proposition IX.2).

Two dimensional anti-de Sitter space and discrete light cone quantization

We realize the two dimensional anti-de Sitter ( AdS 2) space as a Kaluza-Klein reduction of the AdS 3 space in the framework of the discrete light cone quantization (DLCQ). Introducing DLCQ coordinates which interpolate the original (unboosted) coordinates and the light cone coordinates, we discuss that AdS 2/ CFT correspondence can be deduced from the AdS 3/ CFT. In particular, we elaborate on the deformation of WZW model to obtain the boundary theory for the AdS 2 black hole. This enables us to derive the entropy of the AdS 2 black hole from that of the AdS 3 black hole.

A spinning anti-de Sitter wormhole

We construct a (2 + 1)-dimensional spacetime of constant curvature whose spatial topology is that of a torus with one asymptotic region attached. It is also a black hole whose event horizon spins with respect to infinity. An observer entering the hole necessarily ends up at a `singularity'; there are no inner horizons. In the construction we take the quotient of (2 + 1)-dimensional anti-de Sitter space by a discrete group . A key part of the analysis proceeds by studying the action of on the boundary of the spacetime.

Higher spin N = 8 supergravity

The product of two N=8 supersingletons yields an infinite tower of massless states of higher spin in four dimensional anti de Sitter space. All the states with spin s > 1/2 correspond to generators of Vasiliev's super higher spin algebra shs^E (8|4) which contains the D=4, N=8 anti de Sitter superalgebra OSp(8|4). Gauging the higher spin algebra and introducing a matter multiplet in a quasi-adjoint representation leads to a consistent and fully nonlinear equations of motion as shown sometime ago by Vasiliev. We show the embedding of the N=8 AdS supergravity equations of motion in the full system at the linearized level and discuss the implications for the embedding of the interacting theory. We furthermore speculate that the boundary N=8 singleton field theory yields the dynamics of the N=8 AdS supergravity in the bulk, including all higher spin massless fields, in an unbroken phase of M-theory.

Black holes and wormholes in dimensions

A large variety of spacetimes - including the BTZ black holes - can be obtained by identifying points in (2 + 1)-dimensional anti-de Sitter space by means of a discrete group of isometries. We consider all such spacetimes that can be obtained under a restriction to time-symmetric initial data and one asymptotic region only. The resulting spacetimes are non-eternal black holes with collapsing wormhole topologies. Our approach is geometrical, and we discuss in detail the allowed topologies, the shape of the event horizons, topological censorship and trapped curves.

Free equations for massive matter fields in (2 + 1)-dimensional anti-de sitter space from a deformed oscillator algebra

We reformulate free equations of motion for massive spin 0 and spin 1/2 matter fields in 2+1 dimensional anti-de Sitter space in the form of some covariant constantness conditions. The infinite-dimensional representation of the anti-de Sitter algebra underlying this formulation is shown to admit a natural realization in terms of the algebra of deformed oscillators with a deformation parameter related to the parameter of mass.

Making anti-de Sitter black holes

It is known from the work of Bañados et al that a spacetime with event horizons (much like the Schwarzschild black hole) can be obtained from (2 + 1)-dimensional anti-de Sitter space through a suitable identification of points. We point out that this can be done in 3 + 1 dimensions as well. In this way we obtain black holes with event horizons that are tori or Riemann surfaces of genus higher than one. They can have either one or two asymptotic regions (with non-standard topology). Locally, the spacetime is isometric to anti-de Sitter space.

Gauge formulation of the spinning black hole in (2+1)-dimensional anti-de Sitter space.

We compute the group element of SO(2,2) associated with the spinning black hole found by Ba\~nados, Teitelboim and Zanelli in (2+1)-dimensional anti-de Sitter space-time. We show that their metric is built with SO(2,2) gauge invariant quantities and satisfies Einstein's equations with negative cosmological constant everywhere except at $r=0$. Moreover, although the metric is singular on the horizons, the group element is continuous and possesses a kink there.