Showing papers on "Anti-de Sitter space published in 2006"
TL;DR: It is argued 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.
Abstract: 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.
4,395 citations
TL;DR: In this article, it was shown how both particle states and Schwarzschild de Sitter black holes can arise as excitations in a theory of a finite number of fermionic oscillators.
Abstract: We describe progress towards constructing a quantum theory of de Sitter space in four dimensions. In particular we indicate how both particle states and Schwarzschild de Sitter black holes can arise as excitations in a theory of a finite number of fermionic oscillators. The results about particle states depend on a conjecture about algebras of Grassmann variables, which we state, but do not prove.
136 citations
TL;DR: In this paper, a large class of de Sitter vacua of critical string theory from flux compactifications on products of Riemann surfaces is constructed, and it is shown that these effects self-consistently dominate over standard estimates for further quantum corrections, via tuning available from large flux and brane quantum numbers.
Abstract: We construct a large new class of de Sitter (and anti de Sitter) vacua of critical string theory from flux compactifications on products of Riemann surfaces. In the construction, the leading effects stabilizing the moduli are perturbative. We show that these effects self-consistently dominate over standard estimates for further {alpha}{prime} and quantum corrections, via tuning available from large flux and brane quantum numbers.
113 citations
TL;DR: In this paper, a finite action principle for anti-de Sitter gravity is achieved by supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions.
Abstract: A finite action principle for Einstein-Gauss-Bonnet anti--de Sitter gravity is achieved by supplementing the bulk Lagrangian by a suitable boundary term, whose form substantially differs in odd and even dimensions. For even dimensions, this term is given by the boundary contribution in the Euler theorem with a coupling constant fixed, demanding the spacetime to have constant (negative) curvature in the asymptotic region. For odd dimensions, the action is stationary under a boundary condition on the variation of the extrinsic curvature. A well-posed variational principle leads to an appropriate definition of energy and other conserved quantities using the Noether theorem, and to a correct description of black hole thermodynamics. In particular, this procedure assigns a nonzero energy to anti--de Sitter spacetime in all odd dimensions.
96 citations
TL;DR: In this paper, the authors 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.
Abstract: 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.
93 citations
TL;DR: In this paper, the oblique corrections to the electroweak interaction in the holographic model of technicolor theories were studied in terms of a solution to the equations of motion for the anti de Sitter bulk gauge fields.
Abstract: We study the oblique corrections to the electroweak interaction in the holographic model of technicolor theories. The oblique $S$ parameter is expressed in terms of a solution to the equations of motion for the anti de Sitter bulk gauge fields. By analyzing the solution, we establish a rigorous proof that the $S$ parameter is positive and is reduced by walking. We also present the precise numerical values for the $S$ parameter of various technicolor models by solving the equations numerically.
92 citations
TL;DR: 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.
Abstract: 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.
90 citations
TL;DR: For every positively curved Kähler-Einstein manifold in four dimensions, an infinite family of supersymmetric solutions of type IIB supergravity are constructed, dual to two-dimensional conformal field theories with (0,2) supersymmetry.
Abstract: For every positively curved K\"ahler-Einstein manifold in four dimensions, we construct an infinite family of supersymmetric solutions of type IIB supergravity. The solutions are warped products of ${\mathrm{AdS}}_{3}$ 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.
88 citations
TL;DR: In this paper, a first order parent field theory for free higher spin gauge fields on constant curvature spaces was constructed, and the parent theory itself was formulated using a higher dimensional embedding space.
Abstract: We construct a first order parent field theory for free higher spin gauge fields on constant curvature spaces. As in the previously considered flat case, both the original formulation by Fronsdal and the unfolded one by Vasiliev can be reached by two different straightforward reductions. The parent theory itself is formulated using a higher dimensional embedding space. It turns out to be geometrically extremely transparent and free of the intricacies of both of its reductions.
77 citations
TL;DR: In this paper, a class of exact solutions of the Einstein-Maxwell equations is presented which describes an accelerating and rotating charged black hole in an asymptotically de Sitter or anti-de Sitter universe.
Abstract: A class of exact solutions of the Einstein-Maxwell equations is presented which describes an accelerating and rotating charged black hole in an asymptotically de Sitter or anti-de Sitter universe. The metric is presented in a new and convenient form in which the meaning of the parameters is clearly identified, and from which the physical properties of the solution can readily be interpreted.
67 citations
TL;DR: In this article, the effect of multitrace deformations in conformal theories admitting holographic duals in anti-sitter space was studied, and it was shown that these deformations introduce instability both in the bulk AdS space and in the boundary CFT.
Abstract: We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.
01 Jan 2006
TL;DR: In this paper, a simple and short geometrical introduction to the de Sitter and anti-de Sitter universes and briefly comment on their physical meaning is given. But it is worth noting that even if they share important features with Minkowski spacetime, their physical interpretation is quite different and the technical problems to be solved in order to merge De Sitter spacetimes with quantum physics are considerably harder.
Abstract: While celebrating the 100 anniversary of the discovery of special relativity [1], it may not be inappropriate to open a window on the de Sitter universes, as their importance in contemporary physics is gradually increasing. Just to mention two examples, the astronomical evidence for an accelerated expansion of the universe gives a central place to the de Sitter geometry in cosmology [2] while the so-called AdS/CFT correspondence [3] supports a major role for the anti-de Sitter geometry in theoretical physics. From the geometrical viewpoint, among the cousins of Minkowski spacetime (the class of Lorentzian manifolds) de Sitter and anti-de Sitter spacetimes are its closest relatives. Indeed, like the Minkowski spacetime, they are maximally symmetric, i.e. they admit kinematical symmetry groups having ten generators. Maximal symmetry also implies that the curvature is constant (zero in the Minkowski case). Owing to their symmetry, it is possible to give a description of the de Sitter universes without using the machinery of general relativity at all. However, it is worth saying right away that, even if they share important features with Minkowski spacetime, their physical interpretation is quite different and the technical problems to be solved in order to merge de Sitter spacetimes with quantum physics are considerably harder. The aim of this note is to give a simple and short geometrical introduction to the de Sitter and anti-de Sitter universes and to briefly comment on their physical meaning.
TL;DR: In this paper, the authors introduced conformally invariant wave equations in de Sitter space, for scalar and vector fields, and derived the solutions of their wave equations and the related two-point functions in the ambient space notation.
Abstract: Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been calculated. The Hilbert space structure and the field operator, in terms of coordinate independent de Sitter plane waves, have been defined. The construction of the paper is based on the analyticity in the complexified pseudo-Riemannian manifold, presented first by Bros et al. Minkowskian limits of these functions are analyzed. The relation between the ambient space notation and the intrinsic coordinates is then studied in the final stage.
TL;DR: In this paper, upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets on spin manifolds satisfying the dominant energy condition were proved.
Abstract: We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets on spin manifolds satisfying the dominant energy condition. We work in space-dimensions larger than or equal to three, and allow a large class of asymptotic backgrounds, with spherical and non-spherical conformal infinities; in the latter case, a spin-structure compatibility condition is imposed. We give classes of non-trivial examples saturating the inequality. We analyse the borderline case in space-time dimension four: for spherical cross-sections of Scri, equality together with completeness occurs only in anti-de Sitter space-time. On the other hand, in the toroidal case, regular non-trivial initial data sets saturating the bound exist.
TL;DR: In this article, the frequency of the quasinormal modes of linear gravitational perturbations of plane-symmetric anti-de Sitter black holes has been studied in detail.
Abstract: We study in detail the quasinormal modes of linear gravitational perturbations of plane-symmetric anti-de Sitter black holes. The wave equations are obtained by means of the Newman-Penrose formalism and the Chandrasekhar transformation theory. We show that oscillatory modes decay exponentially with time such that these black holes are stable against gravitational perturbations. Our numerical results show that in the large (small) black hole regime the frequencies of the ordinary quasinormal modes are proportional to the horizon radius r{sub +} (wave number k). The frequency of the purely damped mode is very close to the algebraically special frequency in the small horizon limit, and goes as ik{sup 2}/3r{sub +} in the opposite limit. This result is confirmed by an analytical method based on the power series expansion of the frequency in terms of the horizon radius. The same procedure applied to the Schwarzschild anti-de Sitter spacetime proves that the purely damped frequency goes as i(l-1)(l+2)/3r{sub +}, where l is the quantum number characterizing the angular distribution. Finally, we study the limit of high overtones and find that the frequencies become evenly spaced in this regime. The spacing of the frequency per unit horizon radius seems to be a universal quantity, inmore » the sense that it is independent of the wave number, perturbation parity, and black hole size.« less
TL;DR: In this paper, a simple differential equation is derived which describes the evolution of quantum fluctuations of a real scalar field φ in de Sitter space-time, and in the case of massless case the large time behavior of their solution differs by sign from the expression found in earlier papers.
TL;DR: In this paper, a new gauge-invariant criterion for stability against inhomogeneous perturbations of de Sitter space is applied to scenarios of dark energy and inflation in scalar-tensor gravity.
Abstract: A new gauge-invariant criterion for stability against inhomogeneous perturbations of de Sitter space is applied to scenarios of dark energy and inflation in scalar–tensor gravity. The results extend previous studies.
TL;DR: In this paper, a class of higher dimensional solutions to the Einstein-Maxwell equations in d dimensions were presented, which are asymptotically locally flat, de Sitter, or anti-de Sitter spacetimes.
Abstract: We present a class of higher dimensional solutions to Einstein–Maxwell equations in d dimensions. These solutions are asymptotically locally flat, de Sitter, or anti-de Sitter spacetimes. The solutions we obtained depend on two extra parameters other than the mass and the nut charge. These two parameters are the electric charge q and the electric potential at infinity, V, which has non-trivial contribution. We analyse the conditions one can impose to obtain Taub-nut or Taub-bolt spacetimes, including the four-dimensional case. We found that, in the nut case, these conditions coincide with that coming from the regularity of the one-form potential at the horizon. Furthermore, the mass parameter for the higher dimensional solutions depends on the nut charge and the electric charge or the potential at infinity.
TL;DR: In this paper, the authors formulated the notion of the Finsleroid-Finsler space, including the positive-definite as well as indefinite cases, and proposed the associated concepts of angle, scalar product, and the distance function.
TL;DR: In this paper, it was shown that the string scale root alpha' should not be greater than the size of the cosmic horizon in the asymptotic de Sitter space.
Abstract: The cosmological observations provide a strong evidence that there is a positive cosmological constant in our universe and thus the spacetime is asymptotical de Sitter space. The conjecture of gravity as the weakest force in the asymptotical dS space leads to a lower bound on the U(1) gauge coupling g, or equivalently, the positive cosmological constant gets an upper bound rho(V) <= g(2)M(p)(4) in order that the U(1) gauge theory can survive in four dimensions. This result has a simple explanation in string theory, i. e. the string scale root alpha' should not be greater than the size of the cosmic horizon. Our proposal in string theory can be generalized to U(N) gauge theory and gives a guideline to the microscopic explanation of the de Sitter entropy. The similar results are also obtained in the asymptotical anti-de Sitter space.
TL;DR: In this article, it was shown that the Bekenstein bound is not generally valid for free quantum fields in anti-de Sitter spacetime, even if one includes the Casimir energy.
Abstract: We reformulate the Bekenstein bound as the requirement of positivity of the Helmholtz free energy at the minimum value of the function $L=E\ensuremath{-}S/(2\ensuremath{\pi}R)$, where $R$ is some measure of the size of the system. The minimum of $L$ occurs at the temperature $T=1/(2\ensuremath{\pi}R)$. In the case of $n$-dimensional anti-de Sitter spacetime, the rather poorly defined size $R$ acquires a precise definition in terms of the AdS radius $l$, with $R=l/(n\ensuremath{-}2)$. We previously found that the Bekenstein bound holds for all known black holes in AdS. However, in this paper we show that the Bekenstein bound is not generally valid for free quantum fields in AdS, even if one includes the Casimir energy. Some other aspects of thermodynamics in anti-de Sitter spacetime are briefly touched upon.
TL;DR: In this article, a generalized Reissner-Nordstrom-like black hole geometries in a curved brane framework, underlying a noncommutative gauge theory on the brane world, were obtained.
Abstract: We obtain de Sitter (dS) and anti-de Sitter (AdS) generalized Reissner-Nordstrom\char21{}like black hole geometries in a curved ${\mathrm{D}}_{3}$-brane framework, underlying a noncommutative gauge theory on the brane world. The noncommutative scaling limit is explored to investigate a possible tunneling of an AdS vacuum in string theory to dS vacuum in its low energy gravity theory. The Hagedorn transition is invoked into its self-dual gauge theory to decouple the gauge nonlinearity from the dS geometry, which in turn is shown to describe a pure dS vacuum.
TL;DR: The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry as discussed by the authors, which allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti-de Sitter and other models.
Abstract: The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A "Cartan connection" gives a prescription for parallel transport from one "tangent model spacetime" to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as "rolling" the model spacetime along physical spacetime. I explain Cartan geometry, and "Cartan gauge theory", in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its more recent reformulation in terms of BF theory, in the context of Cartan geometry.
TL;DR: In this paper, the Boltzmann factor exp (−βωk) was replaced by exp (ΔS), where S is the entropy of the de Sitter horizon, and the deviation from precise thermality can be regarded as an explicitly calculable correction to the Bunch-Davies state.
Abstract: The Bunch-Davies state appears precisely thermal to a free-falling observer in de Sitter space. However, precise thermality is unphysical because it violates energy conservation. Instead, the true spectrum must take a certain different form, with the Boltzmann factor exp (−βωk) replaced by exp (ΔS), where S is the entropy of the de Sitter horizon. The deviation from precise thermality can be regarded as an explicitly calculable correction to the Bunch-Davies state. This correction is mandatory in that it relies only on energy conservation. The modified Bunch-Davies state leads, in turn, to an (H/Mp)2 modification of the primordial power spectrum of inflationary perturbations, which we determine.
TL;DR: In this article, a family of classical superintegrable Hamiltonians, depending on an arbitrary radial function, which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the (2+1)D anti-de Sitter, Minkowskian and de Sitter spacetimes is constructed.
Abstract: A family of classical superintegrable Hamiltonians, depending on an arbitrary radial function, which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the (2+1)D anti-de Sitter, Minkowskian and de Sitter spacetimes is constructed. Such systems admit three integrals of the motion (besides the Hamiltonian) which are ex- plicitly given in terms of ambient and geodesic polar coordinates. The resulting expressions cover the six spaces in a unified way as these are parametrized by two contraction parameters that govern the curvature and the signature of the metric on each space. Next two maxi- mally superintegrable Hamiltonians are identified within the initial superintegrable family by finding the remaining constant of the motion. The former potential is the superposition of a (curved) central harmonic oscillator with other three oscillators or centrifugal barriers (depending on each specific space), so that this generalizes the Smorodinsky-Winternitz sys- tem. The latter one is a superposition of the Kepler-Coulomb potential with another two oscillators or centrifugal barriers. As a byproduct, the Laplace-Runge-Lenz vector for these spaces is deduced. Furthermore both potentials are analysed in detail for each particular space. Some comments on their generalization to arbitrary dimension are also presented.
TL;DR: In this article, the authors consider globally regular and black holes solutions for the Einstein-Yang-Mills system with negative cosmological constant in $d$-spacetime dimensions and find that the ADM mass of the spherically symmetric solutions generically diverges for $dg4.
Abstract: We consider globally regular and black holes solutions for the Einstein-Yang-Mills system with negative cosmological constant in $d$-spacetime dimensions. We find that the ADM mass of the spherically symmetric solutions generically diverges for $dg4$. Solutions with finite mass are found by considering corrections to the YM Lagrangian consisting in higher order terms of the Yang\char21{}Mills hierarchy. Such systems can occur in the low energy effective action of string theory. A discussion of the main properties of the solutions and the differences with respect to the four dimensional case is presented. The mass of these configurations is computed by using a counterterm method.
TL;DR: In this paper, a covariant phase space for Einstein gravity in dimensions d>=4 with negative cosmological constant was constructed, describing black holes in local equilibrium, and the space-times under consideration are asymptotically anti-de Sitter and admit an inner boundary representing an isolated horizon.
Abstract: We construct a covariant phase space for Einstein gravity in dimensions d>=4 with negative cosmological constant, describing black holes in local equilibrium. Thus, space-times under consideration are asymptotically anti-de Sitter and admit an inner boundary representing an isolated horizon. This allows us to derive a first law of black hole mechanics that involves only quantities defined quasi-locally at the horizon, without having to assume that the bulk space-time is stationary. The first law proposed by Gibbons et al. for the Kerr-AdS family follows from a special case of this much more general first law.
TL;DR: In this paper, upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition were proved.
Abstract: We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in all space-dimensions larger than or equal to three, and allow a large class of asymptotic backgrounds, with spherical and non-spherical conformal infinities; in the latter case, a spin-structure compatibility condition is imposed. We give a large class of non-trivial examples saturating the inequality. We analyse exhaustively the borderline case in space-time dimension four: for spherical cross-sections of Scri, equality together with completeness occurs only in anti-de Sitter space-time. On the other hand, in the toroidal case, regular non-trivial initial data sets saturating the bound exist.
TL;DR: In this paper, a D7-brane probe in AdS5 × S5 background was introduced and the 4d part of the induced metric on D7brane became 4d de-Sitter space (dS4) inside AdS 5 instead of 4d Minkowski space.
Abstract: We introduce a D7-brane probe in AdS5 × S5 background in a way that the 4d part of the induced metric on D7-brane becomes 4d de-Sitter space (dS4) inside AdS5 instead of 4d Minkowski space. Although supersymmetry is completely broken, we obtain a static configuration and show the absence of dynamical tachyonic modes. Following holographic renormalization we renormalize the Dirac-Born-Infeld action of D7-brane and we completely fix the counter terms including finite contributions from the consistency under various limits. Through the AdS/CFT correspondence we study the chiral condensate and meson spectrum of CFT dual theory on dS4 where the energy scale is identified with the direction normal to dS4 space in AdS5. We identify and properly reproduce the finite temperature effects on dS4. Our results support the holographic interpretation of the Randall-Sundrum model with non fine-tuned dS4 brane(s) and the holography between AdSp (or dSp) bulk gravity and CFT on dSp−1 called the (A)dS/dS correspondence.
TL;DR: In this article, the authors studied the collision of two domain walls in five-dimensional asymptotically anti-de Sitter spacetime, which may provide the reheating mechanism of an ekpyrotic brane universe, in which two Bogomol'nyi-Prasad-Sommerfield branes collide and evolve into a hot big bang universe.
Abstract: We study collision of two domain walls in five-dimensional asymptotically anti--de Sitter spacetime. This may provide the reheating mechanism of an ekpyrotic (or cyclic) brane universe, in which two Bogomol'nyi-Prasad-Sommerfield branes collide and evolve into a hot big bang universe. We evaluate a change of scalar field making the domain wall and can investigate the effect of a negative cosmological term in the bulk to the collision process and the evolution of our universe.