Quantum anti-de Sitter space

The quantum anti-de Sitter (AdS) group and the quantum AdS space are discussed. A differential calculus on the quantum AdS space is introduced. A conjugation on the quantum AdS algebra is deduced from the corresponding conjugation on the quantum AdS group. Received: 14 April 1999 / Revised version: 13 December 1999 / Published online: 25 September 2000     

Hadron masses and screening from anti-de Sitter space Wilson loops

We show that in strongly coupled N=4 supersymmetric Yang-Mills conformal theory the binding energy of a heavy and a light quark is independent of the strength of the coupling constant. As a consequence we are able to show that in the presence of light quarks the analog of the QCD string can snap and color charges are screened. The resulting neutral mesons interact with each other only via pion exchange and we estimate the masses of those states.     

Supersymmetries and BPS configurations on anti-de Sitter space

We study supersymmetry breaking due to the presence of branes on anti-de Sitter space and obtain conditions for brane orientations not to break too many supersymmetries. Using the conditions, we construct a brane configuration corresponding to a baryon in large N gauge theory, and it is shown that the baryon is a marginal bound state of quarks, as is expected from supersymmetry.     

Supersymmetric 3D anti-de Sitter space solutions of type IIB supergravity

For every positively curved K?hler-Einstein manifold in four dimensions, we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of AdS3 with a compact seven-dimensional manifold and have nonvanishing five-form flux. Via the anti-de Sitter/conformal field theory correspondence, the solutions are dual to two-dimensional conformal field theories with (0,2) supersymmetry. The corresponding central charges are rational numbers.     

Gott time machines in anti-de Sitter space

In 1991 Gott presented a solution of Einstein's field equations in 2+1 dimensions with =0 that contained closed timelike curves (ctc's). This solution was remarkable because at first it did not seem to be unphysical in any other respect. Later, however, it was shown that Gott's solution is tachyonic in a certain sense. Here the case <0 is discussed. We show that it is also possible to constructctc's in this case, in a way analogous to that used by Gott. We also show a special case of this construction to be tachyonic. <0 means that we are dealing with anti-de Sitter space, and since the CTC-construction necessitates some understanding of its structure, a few pages are devoted to this subject.     

Generic cosmic-censorship violation in anti-de Sitter space

We consider (four-dimensional) gravity coupled to a scalar field with potential V(phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti-de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of cosmic censorship in asymptotically flat spacetimes, but we do not have definite results.     

Bjorken flow from an anti-de Sitter space Schwarzschild black hole

We consider a large black hole in asymptotically anti-de Sitter spacetime of arbitrary dimension with a Minkowski boundary. By performing an appropriate slicing as we approach the boundary, we obtain via holographic renormalization a gauge theory fluid obeying Bjorken hydrodynamics in the limit of large longitudinal proper time. The metric we obtain reproduces to leading order the metric recently found as a direct solution of the Einstein equations in five dimensions. Our results are also in agreement with recent exact results in three dimensions.     

Evolutes of spacelike hypersurfaces in anti-de Sitter space

We study spacelike hypersurfaces in anti-de Sitter space from the view point of the Lagrangian/Legendrian singularity theory.     

Thermodynamics of black holes in anti-de Sitter space

The Einstein equations with a negative cosmological constant admit black hole solutions which are asymptotic to anti-de Sitter space. Like black holes in asymptotically flat space, these solutions have thermodynamic properties including a characteristic temperature and an intrinsic entropy equal to one quarter of the area of the event horizon in Planck units. There are however some important differences from the asymptotically flat case. A black hole in anti-de Sitter space has a minimum temperature which occurs when its size is of the order of the characteristic radius of the anti-de Sitter space. For larger black holes the red-shifted temperature measured at infinity is greater. This means that such black holes have positive specific heat and can be in stable equilibrium with thermal radiation at a fixed temperature. It also implies that the canonical ensemble exists for asymptotically anti-de Sitter space, unlike the case for asymptotically flat space. One can also consider the microcanonical ensemble. One can avoid the problem that arises in asymptotically flat space of having to put the system in a box with unphysical perfectly reflecting walls because the gravitational potential of anti-de Sitter space acts as a box of finite volume.     

High energy field theory in truncated anti-de Sitter space

In this Letter we show that in five-dimensional anti-de Sitter (AdS) space truncated by boundary branes, effective field theory techniques are reliable at high energy (much higher than the scale suggested by the Kaluza-Klein mass gap), provided one computes suitable observables. We argue that in the model of Randall and Sundrum for generating the weak scale from the AdS warp factor, the high energy behavior of gauge fields can be calculated in a cutoff independent manner, provided one restricts Green's functions to external points on the Planck brane. Using the AdS/CFT (conformal field theory) correspondence, we calculate the one-loop correction to the Planck brane gauge propagator due to charged bulk fields. These effects give rise to nonuniversal logarithmic energy dependence for a range of scales above the Kaluza-Klein gap.     

Gauss-Bonnet solution with a cloud of strings in de Sitter and anti-de Sitter space

In this study,we investigate exact spherically symmetric Gauss-Bonnet black hole solutions surrounded by a cloud of string fluid with the cosmological constant in D> 4 dimensions.Both charged and uncharged cases are considered.We focus on the de Sitter solutions in the main text and provide the anti-de Sitter solutions in the appendix.We analyze the features of event horizons and thermodynamic properties of the black hole solutions.The mass,Hawking temperature,thermal stability,and phase tran...     

Conformally coupled scalars, instantons, and vacuum instability in 4D anti-de Sitter space

We show that a scalar field conformally coupled to AdS gravity in four dimensions with a quartic self-interaction can be embedded into M theory. The holographic effective potential is exactly calculated, allowing us to study nonperturbatively the stability of AdS4 in the presence of the conformally coupled scalar. It is shown that there exists a one-parameter family of conformal scalar boundary conditions for which the boundary theory has an unstable vacuum. In this case, the bulk theory has instanton solutions that mediate the decay of the AdS4 space. These results match nicely with the vacuum structure and the existence of instantons in an effective three-dimensional boundary model.     

Asymptotically anti-de Sitter spaces

Asymptotically anti-de Sitter spaces are defined by boundary conditions on the gravitational field which obey the following criteria: (i) they are O(3, 2) invariant; (ii) they make the O(3, 2) surface integral charges finite; (iii) they include the Kerr-anti-de Sitter metric. An explicit expression of the O(3, 2) charges in terms of the canonical variables is given. These charges are shown to close in the Dirac brackets according to the anti-de Sitter algebra. The results are extended to the case ofN=1 supergravity. The coupling to gravity of a third-rank, completely antisymmetric, abelian gauge field is also considered. That coupling makes it possible to vary the cosmological constant and to compare the various anti-de Sitter spaces which are shown to have the same energy.On leave from Département de Physique, Université Libre de Bruxelles, BelgiumChercheur qualifié du Fonds National Belge de la Recherche Scientifique     

Anyonic strings and membranes in anti-de Sitter space and dual Aharonov-Bohm effects

It is observed that strings in AdS(5) x S(5) and membranes in AdS(7) x S(4) exhibit long range phase interactions. Two well separated membranes dragged around one another in anti-de Sitter space (AdS) acquire phases of 2 pi/N. The same phases are acquired by a well separated F and D string dragged around one another. The phases are shown to correspond to both the standard and a novel type of Aharonov-Bohm effect in the dual field theory.     

Entanglement entropy of black holes and anti-de Sitter space/conformal-field-theory correspondence

A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L(2)lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted.     

Lorentz boosts in de Sitter and anti-de Sitter space-times

Symmetries of de Sitter and anti-de Sitter space-times are discussed. In particular, Lorentz boosts, which appear to be given previously only in the infinitesimal form, are presented here in closed finite forms.Dedicated to the memory of Professor Jozef Kvasnica.I would like to thank Prof. Jií Biák and Dr. Hans-Jürgen Schmidt for useful discussions.     

Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.