Five-dimensional Anti-de Sitter Research Articles

Completeness of non-normalizable modes

We establish the completeness of some characteristic sets of non-normalizable modes by constructing fully localized square steps out of them, with each such construction expressly displaying the Gibbs phenomenon associated with trying to use a complete basis of modes to fit functions with discontinuous edges. As well as being of interest in and of itself, our study is also of interest to the recently introduced large extra dimension brane-localized gravity program of Randall and Sundrum, since the particular non-normalizable mode bases that we consider (specifically the irregular Bessel functions and the associated Legendre functions of the second kind) are associated with the tensor gravitational fluctuations which occur in those specific brane worlds in which the embedding of a maximally four-symmetric brane in a five-dimensional anti-de Sitter bulk leads to a warp factor which is divergent. Since the brane-world massless four-dimensional graviton has a divergent wave function in these particular cases, its resulting lack of normalizability is thus not seen to be any impediment to its belonging to a complete basis of modes, and consequently its lack of normalizability should not be seen as a criterion for not including it in the spectrum of observable modes. Moreover, because the divergent modes we consider form complete bases, we can even construct propagators out of them in which these modes appear as poles with residues which are expressly finite. Thus even though normalizable modes appear in propagators with residues which are given as their finite normalization constants, non-normalizable modes can just as equally appear in propagators with finite residues too -- it is just that such residues will not be associated with bilinear integrals of the modes.

Black hole as emergent holographic geometry of weakly interacting hot Yang-Mills gas

We demonstrate five-dimensional anti-de Sitter black hole emerges as dual geometry holographic to weakly interacting N=4 superconformal Yang-Mills theory. We first note that an ideal probe of the dual geometry is the Yang-Mills instanton, probing point by point in spacetime. We then study instanton moduli space at finite temperature by adopting Hitchin's proposal that geometry of the moduli space is definable by Fisher-Rao "information geometry". In Yang-Mills theory, the information metric is measured by a novel class of gauge-invariant, nonlocal operators in the instanton sector. We show that the moduli space metric exhibits (1) asymptotically anti-de Sitter, (2) horizon at radial distance set by the Yang-Mills temperature, and (3) after Wick rotation of the moduli space to the Lorentzian signature, a singularity at the origin. We argue that the dual geometry emerges even for rank of gauge groups of order unity and for weak `t Hooft coupling.

Supersymmetric AdS5 solutions of type IIB supergravity

We analyse the most general bosonic supersymmetric solutions of type IIB supergravity whose metrics are warped products of five-dimensional anti-de Sitter space (AdS5) with a five-dimensional Riemannian manifold M5. All fluxes are allowed consistent with SO(4, 2) symmetry. We show that the necessary and sufficient conditions can be phrased in terms of a local identity structure on M5. For a special class, with constant dilaton and vanishing axion, we reduce the problem to solving a second-order nonlinear ODE. We find an exact solution of the ODE which reproduces a solution first found by Pilch and Warner. A numerical analysis of the ODE reveals an additional class of local solutions giving complete metrics on S5 but with three-form flux and Killing spinors that are not globally defined.

Induced gravity and universe creation on the domain wall in five-dimensional space-time

We present a model with a strong fermion self-interaction and an induced gravitational interaction in five-dimensional space-time. In the strong-coupling regime, this model develops a spontaneous breaking of translational invariance, which results in localizing light particles on the (3+1)-dimensional domain wall embedded in the anti-de Sitter five-dimensional space-time. We obtain the corresponding low-energy effective action and investigate kink-type vacuum solutions in a quasiflat Riemannian metric. We discuss the physics of light particles in 3+1 dimensions and establish the fundamental relations between the induced gravitational constant and both the curvature in the five-dimensional anti-de Sitter space-time and the Newton gravitational constant of our universe.

Kantowski–Sachs universe

We consider the brane Kantowski?Sachs universe when bulk space is five-dimensional anti-de Sitter space. The corresponding cosmological equations with perfect fluid are written. For several specific choices of relation between energy and pressure, the behaviour of scale factors at early time is found. In particular for , Kantowski?Sachs brane cosmology is modified to become the isotropic one, while for it remains the anisotropic cosmology in the process of evolution.

THE GENERALIZED UNCERTAINTY PRINCIPLE AND CORRECTIONS TO THE CARDY–VERLINDE FORMULA IN SAdS5 BLACK HOLES

In this paper, we investigate a possible modification to the temperature and entropy of five-dimensional Schwarzschild anti-de Sitter black holes due to the incorporation of stringy corrections to the modified uncertainty principle. Then, we subsequently argue for corrections to the Cardy–Verlinde formula in order to account for the corrected entropy. Then, we show that one can taking into account the generalized uncertainty principle corrections of the Cardy–Verlinde entropy formula by just redefining the Virasoro operator L0 and the central charge c.

Tensorial perturbations in a brane with induced gravity

We calculate the amplitude of gravitational waves produced by inflation on a de Sitter brane embedded in five-dimensional anti-de Sitter bulk space-time, extending previous calculations in Randall-Sundrum type cosmology to include the effect of induced gravity corrections on the brane. These corrections arise via a term in the brane action that is proportional to the brane Ricci scalar. We find that, as in the Randall-Sundrum case, there is a mass gap between the discrete zero-mode and a continuum of massive bulk modes, which are too heavy to be excited during inflation. We give the normalisation of the zero-mode as a function of the Hubble rate on the brane and are thus able to calculate the high energy correction to the spectrum of gravitational wave (tensor) modes excited on large scales during inflation from initial vacuum fluctuations on small scales.

METASTABLE MASSIVE GRAVITONS FROM AN INFINITE EXTRA DIMENSION

Motivated by stringy considerations, Randall and Sundrum have proposed a model where all the fields and particles of physics, save gravity, are confined on a four-dimensional brane embedded in five-dimensional anti-de Sitter space. Their scenario features a stable bound state of bulk gravity waves and the brane that reproduces standard general relativity. We demonstrate that in addition to this zero-mode, there is also a discrete set of metastable bound states that behave like massive four-dimensional gravitons which decay by tunneling into the bulk. These are resonances of the bulk-brane system akin to black hole quasinormal modes — as such, they give rise to the dominant corrections to four-dimensional gravity. The phenomenology of braneworld perturbations is greatly simplified when these resonant modes are taken into account, which is illustrated by considering gravitational radiation emitted from nearby sources and early universe physics.

Gravitational backreaction of anti-D branes in the warped compactification

We derive a low-energy effective theory for gravity with anti-D branes, which are essential to get de Sitter solutions in the type IIB string-warped compactification, by taking account of gravitational backreactions of anti-D branes. In order to see the effects of the self-gravity of anti-D branes, a simplified model is studied where a five-dimensional anti-de Sitter (AdS) spacetime is realized by the bulk cosmological constant and the 5-form flux, and anti-D branes are coupled to the 5-form field by Chern–Simon terms. The AdS spacetime is truncated by introducing UV and IR cut-off branes like the Randall–Sundrum model. We derive an effective theory for gravity on the UV brane and reproduce the familiar result that the tensions of the anti-D branes give potentials suppressed by the fourth power of the warp factor at the location of the anti-D branes. However, in this simplified model, the potential energy never inflates the UV brane, although the anti-D branes are inflating. The UV brane is dominated by dark radiation coming from the projection of the five-dimensional Weyl tensor, unless the moduli fields for the anti-D branes are stabilized. We comment on the possibility of avoiding this problem in a realistic string theory compactification.

VACUUM POLARIZATION IN AN ANTI-DE SITTER SPACE AS AN ORIGIN FOR A COSMOLOGICAL CONSTANT IN A BRANE WORLD

We show that the vacuum polarization of quantum fields in an anti-de Sitter space can naturally give rise to a small but nonzero cosmological constant in a brane world living in it. To explain the extremely small ratio of mass density in the cosmological constant to the Planck mass density in our universe (≈10-123) as suggested by cosmological observations, all we need is a four-dimensional brane world (our universe) living in a five-dimensional anti-de Sitter space with a curvature radius r0~10-3 cm and a fundamental Planck energy M P ~109 GeV , and a scalar field with a mass [Formula: see text]. Probing gravity down to a scale ~10-3 cm, which is attainable in the near future, will provide a test of the model.

Evolution of gravitational waves in the high-energy regime of brane-world cosmology

We discuss the evolution of gravitational waves (GWs) after inflation in a brane-world cosmology embedded in five-dimensional anti-de Sitter (AdS5) bulk spacetime. In a brane-world scenario, the evolution of GWs is affected by the non-standard cosmological expansion and the excitation of the Kaluza–Klein (KK) modes, which are significant in the high-energy regime of the universe. We numerically solve the wave equation of GWs in the Poincaré coordinates of the AdS5 spacetime. Using a plausible initial condition from inflation, we find that, while the behavior of GWs in the bulk is sensitive to the transition time from inflation to the radiation-dominated epoch, the amplitude of GWs on the brane is insensitive to this time if the transition occurs early enough before horizon reentry. As a result, the amplitude of GWs is suppressed by the excitation of KK-modes and the effect may compensate the enhancement of the GWs by the non-standard cosmological expansion. Based on this, the influence of the high-energy effects on the GW backgrounds is discussed.

Gravitational waves from brane-world inflation with induced gravity

We calculate the amplitude of gravitational waves produced by inflation on a de Sitter brane embedded in five-dimensional anti-de Sitter bulk spacetime, extending previous calculations in Randall-Sundrum type cosmology to include the effect of induced gravity corrections on the brane. These corrections arise via a term in the brane action that is proportional to the brane Ricci scalar. We find that, as in the Randall-Sundrum case, there is a mass gap between the discrete zero-mode and a continuum of massive bulk modes, which are too heavy to be excited during inflation. We give the normalization of the zero-mode as a function of the Hubble rate on the brane and are thus able to calculate the high energy correction to the spectrum of gravitational wave (tensor) modes excited on large scales during inflation from initial vacuum fluctuations on small scales. We also calculate the amplitude of density (scalar) perturbations expected due to inflaton fluctuations on the brane, and show that the usual four-dimensional consistency relation for the tensor/scalar ratio remains valid for brane inflation with induced gravity corrections.

Multiple-scales analysis of cosmological perturbations in brane-worlds

We present a new approximation method for solving the equations of motion for cosmological tensor perturbations in a Randall-Sundrum brane-world model of the type with one brane in a five-dimensional anti-de Sitter spacetime. This method avoids the problem of coordinate singularities inherent in some methods. At leading-order, the zero-mode solution replicates the evolution of perturbations in a four-dimensional Friedmann-Robertson-Walker universe in the absence of any tensor component to the matter perturbation on the brane. At next order, there is a mode-mixing effect, although, importantly, the zero-mode does not source any other modes.

Supersymmetric AdS5 solutions of M-theory

We analyse the most general supersymmetric solutions of D = 11 supergravity consisting of a warped product of five-dimensional anti-de Sitter space with a six-dimensional Riemannian space M6, with 4-form flux on M6. We show that M6 is partly specified by a one-parameter family of four-dimensional Kähler metrics. We find a large family of new explicit regular solutions where M6 is a compact, complex manifold which is topologically a 2-sphere bundle over a four-dimensional base, where the latter is either (i) Kähler–Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki–Einstein spaces which includes . Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.

Evolution of gravitational waves from inflationary brane-world: numerical study of high-energy effects

We study the evolution of gravitational waves (GWs) after inflation in a brane-world cosmology embedded in five-dimensional anti-de Sitter space–time. Contrary to the standard four-dimensional results, the GWs at the high-energy regime in brane-world model suffer from the effects of the non-standard cosmological expansion and the excitation of the Kaluza–Klein modes (KK-modes), which can affect the amplitude of stochastic gravitational wave background significantly. To investigate these two high-energy effects quantitatively, we numerically solve the wave equation of the GWs in the radiation dominated epoch at relatively low-energy scales. We show that the resultant GWs are suppressed by the excitation of the KK modes. The created KK modes are rather soft and escape away from the brane to the bulk gravitational field. The results are also compared to the semi-analytic prediction from the low-energy approximation and the evolved amplitude of GWs on the brane reasonably matches the numerical simulations.

Supersymmetric solutions of minimal gauged supergravity in five dimensions

All purely bosonic supersymmetric solutions of minimal gauged supergravity in five dimensions are classified. The solutions fall into two classes depending on whether the Killing vector constructed from the Killing spinor is timelike or null. When it is timelike, the solutions are determined by a four-dimensional K\ahler base manifold, up to an antiholomorphic function, are necessarily not static, and generically preserve 1/2 of the supersymmetry. When it is null we provide a precise prescription for constructing the solutions and we show that they generically preserve 1/4 of the supersymmetry. We show that five-dimensional anti-de Sitter space $({\mathrm{AdS}}_{5})$ is the unique maximally supersymmetric configuration. The formalism is used to construct some new solutions, including a nonsingular deformation of ${\mathrm{AdS}}_{5},$ which can be uplifted to obtain new solutions of type IIB supergravity.

Tensorial perturbations in the bulk of inflating brane worlds

In this paper we consider the stability of some inflating brane-world models in quantum cosmology. It is shown that whereas the singular model based on the construction of inflating branes from Euclidean five-dimensional anti-de Sitter space is unstable to tensorial cosmological perturbations in the bulk, the nonsingular model which uses a five-dimensional asymptotically anti-de Sitter wormhole to construct the inflating branes is stable to these perturbations.

Evolution of gravitational waves in Randall–Sundrum cosmology

We investigate the evolution of gravitational wave perturbations about a brane cosmology embedded in a five-dimensional anti-de Sitter bulk. During slow-roll inflation in a Randall–Sundrum brane-world, thezero mode of the five-dimensional graviton is generated, while themassive modes remain in their vacuum state. When the zero modere-enters the Hubble radius during radiation domination, massivemodes are generated. We show that modes decouple in the low-energy/near-brane limit and develop perturbative techniques to calculatethe mode-mixing at finite energy.

Observational constraints on dark radiation in brane cosmology

We analyze the observational constraints on brane-world cosmology whereby the universe is described as a three-brane embedded in a five-dimensional anti-de Sitter space. In this brane-universe cosmology, the Friedmann equation is modified by the appearance of extra terms which derive from existence of the extra dimensions. In the present work we concentrate on the “dark radiation” term which diminishes with cosmic scale factor as a −4. We show that, although the observational constraints from primordial abundances allow only a small contribution when this term is positive, a much wider range of negative between the observed primordial 4He and D abundances. We also discuss the possible constraints on this term from the power spectrum of CMB anisotropies in the limit of negligible cosmological perturbation on the brane world. We show that BBN limits the possible contribution from dark radiation just before the e + e − aniihilation epoch to lie between −123% and +11% of the background photon energy density. Combining this with the CMB constraint reduces this range to between −41% and +10.5% at the 2σ confidence level.

GRAVITATIONAL TRAPPING FOR EXTENDED EXTRA DIMENSION

The solution of Einstein's equations for 4-brane embedded in five-dimensional Anti-de Sitter space–time is found. It is shown that the cosmological constant can provide the existence of ordinary four-dimensional Newton's law and trapping of a matter on the brane.