Five-dimensional Anti-de Sitter Spacetime Research Articles

Fragmentation of AdS5-Kerr black holes

Black hole spacetimes asymptotic to five-dimensional anti-de Sitter spacetime are of great interest in connection with the string-gauge duality. In the rotating case, such black holes tend to become unstable, in several different ways, if their specific angular momenta fall in certain ranges. Here we consider the well-known Emparan-Myers fragmentation instability for singly rotating AdS5-Kerr black holes, paying particular attention to the case where the specific angular momentum exceeds the asymptotic AdS5 curvature length scale.

Topological Effects in a Fermionic Condensate Induced by a Cosmic String and Compactification on the AdS Bulk

In this paper, we analyzed the fermionic condensate (FC) associated with a massive fermionic field on a five-dimensional anti-de Sitter (AdS) spacetime in the presence of a cosmic string taking into account a magnetic flux running along its core. In addition, a compactified dimension was considered. Due to this compactification, the FC is expressed in terms of two distinct contributions: the first one corresponds to the geometry without compactification, and the second one is induced by the compactification. Depending on the values of the physical parameters, the total FC can be positive or negative. As a limiting case, the expression for the FC on locally Minkowski spacetime was derived. It vanishes for a massless fermionic field, and the nonzero FC on the AdS background space in the massless case is an effect induced by gravitation. This shows that the gravitational field may essentially influence the parameter space for phase transitions. For a massive field, the FC diverges on the string as the inverse cube of the proper distance from the string. In the case of a massless field, depending on the magnetic flux along the string and planar angle deficit, the limiting value of the FC on the string can be either finite or infinite. At large distances, the decay of the FC as a function of the distance from the string is a power law for both cases of massive and massless fields. For a cosmic string on the Minkowski bulk and for a massive field, the decay is exponential. The topological part in the FC vanishes on the AdS boundary. We show that the FCs coincide for the fields realizing two inequivalent irreducible representations of the Clifford algebra. In the special case of the zero planar angle deficit, the results presented in this paper describe Aharonov–Bohm-type effects induced by magnetic fluxes in curved spacetime.

Anomaly inflow and holography

We systematically study the perturbative anomaly inflow by the bulk Chern-Simons (CS) theory in a slice of five-dimensional anti-de Sitter spacetime (AdS5). The introduction of UV and IR 3-branes makes the anomaly story remarkably rich and many interesting aspects can be obtained, including weakly gauging and spontaneous symmetry breaking of the global symmetries of the dual 4D CFT. Our main contribution is to provide a unified and comprehensive discussion of the subject, together with a detailed description of the dual CFT picture for each case. To this end, we employ a gauge-fixed effective action suitable for a holographic study, which allows us to incorporate general UV and IR boundary conditions (BCs). As part of the process, we reproduce many known results in the literature, such as ’t Hooft anomaly matching for unbroken symmetry (Neumann IR-BC) and (gauged) Wess-Zumino-Witten (WZW) action for broken symmetry (IR-BC breaks the bulk group G → H). In addition, we show that anomaly matching occurs for ABJ anomalies as well as ’t Hooft anomalies, which suggests anomalies inflowed from the bulk CS theory are necessarily free of mixed anomalies with the confining gauge force of the 4D dual CFT. In the case of broken symmetry, we prove that the “would-be” Goldstone bosons associated with the weakly gauged symmetry are completely removed by a proper field redefinition, provided the anomaly from the bulk is exactly cancelled by the boundary contribution, hence confirming the standard expectation. Moreover, we present a holographic formulation of Witten’s argument for the quantization condition for the WZW action, and argue in favor of an alternative way to obtain the same condition using a “deformed” theory (different BCs). We work out several examples, including a product group with mixed anomaly, and identify the corresponding dual CFT picture. We consider a fully general case typically arising in the context of dynamical electroweak symmetry breaking.

Tidal Love numbers of braneworld black holes and wormholes

We study the tidal deformations of various known black hole and wormhole solutions in a simple context of warped compactification -- Randall-Sundrum theory in which the four-dimensional spacetime geometry is that of a brane embedded in five-dimensional Anti-de Sitter spacetime. The linearized gravitational perturbation theory generically reduces to either an inhomogeneous second-order ODE or a homogeneous third-order ODE of which indicial roots associated with an expansion about asymptotic infinity can be related to Tidal Love Numbers. We describe various tidal-deformed metrics, classify their indicial roots, and find that in particular the quadrupolar TLN is generically non-vanishing. Thus it could be a signature of a braneworld by virtue of its potential appearance in gravitational waveforms emitted in binary merger events.

Probing extra dimension through gravitational wave observations of compact binaries and their electromagnetic counterparts

The future gravitational wave (GW) observations of compact binaries and their possible electromagnetic counterparts may be used to probe the nature of the extra dimension. It is widely accepted that gravitons and photons are the only two completely confirmed objects that can travel along null geodesics in our four-dimensional space-time. However, if there exist extra dimensions and only GWs can propagate freely in the bulk, the causal propagations of GWs and electromagnetic waves (EMWs) are in general different. In this paper, we study null geodesics of GWs and EMWs in a five-dimensional anti-de Sitter space-time in the presence of the curvature of the universe. We show that for general cases the horizon radius of GW is longer than EMW within equal time. Taking the GW150914 event detected by the Advanced Laser Interferometer Gravitational-Wave Observatory and the X-ray event detected by the Fermi Gamma-ray Burst Monitor as an example, we study how the curvature k and the constant curvature radius l affect the horizon radii of GW and EMW in the de Sitter and Einstein-de Sitter models of the universe. This provides an alternative method for probing extra dimension through future GW observations of compact binaries and their electromagnetic counterparts.

Lifshitz effects on holographic p-wave superfluid

In the probe limit, we numerically build a holographic p-wave superfluid model in the four-dimensional Lifshitz black hole coupled to a Maxwell-complex vector field. We observe the rich phase structure and find that the Lifshitz dynamical exponent z contributes evidently to the effective mass of the matter field and dimension of the gravitational background. Concretely, we obtain that the Cave of Winds appeared only in the five-dimensional anti-de Sitter (AdS) spacetime, and the increasing z hinders not only the condensate but also the appearance of the first-order phase transition. Furthermore, our results agree with the Ginzburg–Landau results near the critical temperature. In addition, the previous AdS superfluid model is generalized to the Lifshitz spacetime.

Stability of charged solitons and formation of boson stars in five-dimensional anti-de Sitter spacetime

We study the stability of charged solitons in five-dimensional anti-de Sitter (AdS) spacetime. We show that for appropriate choices of the parameters of the model these solutions become unstable to form scalar hair. We find that the existence of charged solitons with scalar hair depends crucially on the charge and the mass of the scalar field. We investigate the dependence of the spectrum of solutions on the mass of the scalar field in detail. For positive mass of the scalar field, the hairy solitons can be interpreted as charged boson stars. We find that for a sufficiently small value of the charge of the scalar field a ‘forbidden band’ of the boson star’s mass and charge exists, while all our results indicate that—contrary to the asymptotically flat spacetime case—boson stars in asymptotic AdS can have arbitrarily large charge and mass.

Modulated instability in five-dimensional U(1) charged AdS black hole with R2-term

We study the effect of R**2 term to the modulated instability in the U(1) charged black hole in five-dimensional Anti-de Sitter space-time. We consider the first-order corrections of R**2 term to the background and the linear order perturbations in the equations of motion. From the analysis, we clarify the effect of R**2 term in the modulated instability, and conclude that fluctuations are stable in the whole bulk in the range of values the coefficient of R**2 term can take.

AdS5 supersymmetry in N = 1 superspace

We use N=1 superspace to construct the supersymmetric matter couplings of vector and hyper multiplets in a five-dimensional anti-de Sitter spacetime background. For hypermultiplets, we find that AdS_5 supersymmetry requires the scalar fields to lie on a hyper-Kahler manifold endowed with a certain type of holomorphic Killing vector.

Stability of the warped black string with nontrivial topology in five-dimensional anti–de Sitter spacetime

We investigate the stability of a new warped black string with nontrivial topologies in five-dimensional anti--de Sitter spacetime. After studying the linear gravitational perturbation, we find that this black string is unstable when the Kaluza-Klein mass falls in a certain range, and the instability exists for all topological spacetimes.

Standard model of fermions on the domain wall in five-dimensional space-time

The mechanism of generation of the Standard Model for fermions on the domain wall in five-dimensional space-time is presented. As a result of self-interaction of five-dimensional fermions and gravity induced by matter fields, in the strong coupling regime, in the model there arises a spontaneous translational symmetry breaking, which leads to localization of light particles on a 3 + 1-dimensional domain wall (“3-brane”) that is embedded into a five-dimensional anti-de Sitter space-time (AdS5). Appropriate low-energy, effective action, classical kink-like vacuum configurations for the gravity and scalar fields are investigated. Mass spectra for light composite particles and their coupling constants interaction in ultra-low-energy, which localize on the brane, are explored. We establish estimates of characteristic scales and constants interactions of the model and also a relation between the bulk five-dimensional gravitational constant, curvature of AdS5 space-time, and brane Newton’s constants. The induced cosmological constant on the brane exactly vanishes in all orders of the theory perturbation. We find out that scalar interaction is strongly suppressed at ultra-low-energy, and the brane fluctuations (branons) are suitable “sterile” canditates for explanation of the phenomenon of Dark Matter. Bibliography: 21 titles.

Gravitating multidefects from higher dimensions

Warped configurations admitting pairs of gravitating defects are analyzed. After devising a general method for the construction of multidefects, specific examples are presented in the case of higher-dimensional Einstein-Hilbert gravity. The obtained profiles describe diverse physical situations such as (topological) kink-antikink systems, pairs of nontopological solitons, and bound configurations of a kink and of a nontopological soliton. In all the mentioned cases the geometry is always well behaved (all relevant curvature invariants are regular) and tends to five-dimensional anti-de Sitter space-time for large asymptotic values of the bulk coordinate. Particular classes of solutions can be generalized to the framework where the gravity part of the action includes, as a correction, the Euler-Gauss-Bonnet combination. After scrutinizing the structure of the zero modes, the obtained results are compared with conventional gravitating configurations containing a single topological defect.

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.

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.

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.

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.

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.

Shortcuts in the fifth dimension

If our Universe is a three-brane embedded in a five-dimensional anti-deSitter spacetime, in which matter is confined to the brane and gravity inhabits an infinite bulk space, then the causal propagation of luminous and gravitational signals is in general different. A gravitational signal traveling between two points on the brane can take a ``shortcut'' through the bulk, and appear quicker than a photon traveling between the same two points along a geodesic on the brane. Similarly, in a given time interval, a gravitational signal can propagate farther than a luminous signal. We quantify this effect, and analyze the impact of these shortcuts through the fifth dimension on cosmology.

Evolution of cosmological perturbations in a brane-universe.

In our present Letter, we analyze the impact of the existence of extra dimensions on cosmology, in particular, on the evolution of cosmological perturbations. For a five-dimensional anti-de Sitter spacetime where ordinary matter is confined to a brane-universe, the equations governing the cosmological perturbations are presented in a form very close to the equations of standard cosmology. Two types of corrections appear: corrections due to the unconventional evolution of the homogeneous solution, which change the background-dependent coefficients of the equations, and corrections due to the curvature along the fifth dimension, which act as source terms in the evolution equations.

Gravitational waves from inflation on the brane

We discuss the evolution of gravitational waves in a brane-world cosmology embedded in five-dimensional anti-de Sitter spacetime. We show that during slow-roll inflation, modelled as a period of quasi-de Sitter expansion on the brane, there is a discrete normalizable massless graviton mode. There is a mass gap due to the expansion, above which there is a continuum of massive modes. Only the massless mode is `light' compared with the Hubble scale during inflation, leading to the production of classical perturbations on large scales from vacuum fluctuations on small scales. We calculate the amplitude of these fluctuations at horizon-crossing and show that the standard four-dimensional result is recovered at low energies, but the amplitude of the perturbations is enhanced at high energies.