A generalized two-brane Randall-Sundrum warped braneworld model admits of solutions of the warp factor for both positive or negative cosmological constant on the visible 3-brane which can resolve the naturalness problem in connection with the fine tuning of Higgs mass in the standard model of elementary particles. To explore the location of the standard model fermions in such a generalized warped model, we, in this work, determine the dependence of the localization profile of a bulk fermion on the brane cosmological constant brane tension and the bulk fermion mass. Our results reveal that for a positive and small value of the induced cosmological constant a bulk fermion is localized close to the brane. On the other hand for a visible brane with negative cosmological constant and positive tension, the fermions are localized inside the bulk leading to phenomenologically interesting possibilities.
We modify Randall-Sundrum model of brane-world (with two branes) by adding the scalar curvature squared term in five dimensions. We find that it does not destabilize Randall-Sundrum solution to the hierarchy problem of the Standard Model in particle physics.
We suggest a modification of the Randall-Sundrum scenario which doesn't involve branes with the negative tensions. In our scenario four-dimensional brane world is produced by the external field. The probability of this process is calculated and the physical features of the model are discussed.
In the generalized Randall-Sundrum warped brane-world model the cosmological constant induced on the visible brane can be positive or negative. In this paper we investigate profiles of vacuum expectation value of the bulk scalar field under general Dirichlet andNeumann boundary conditions in the generalized warped brane-worldmodel.We showthat the VEVprofiles generally depend on the value of the brane cosmological constant. We find that the VEV profiles of the bulk scalar field for a visible brane with negative cosmological constant and positive tension are quite distinct fromthose of Randall-S…
We derive the second variation Lagrangian of the Randall-Sundrum model with two branes, study its gauge invariance and diagonalize it in the unitary gauge. We also show that the effective four-dimensional theory looks different on different branes and calculate the observable mass spectra and the couplings of the physical degrees of freedom of 5-dimensional gravity to matter.
Bulk antisymmetric tensor fields of different ranks have been studied in the context of a generalized Randall-Sundrum model with a non-vanishing induced cosmological constant on the visible brane. It is shown that instead of the usual exponential suppression of the couplings of the zero modes of these bulk fields with the brane fermions in the original Randal-Sundrum model, here the couplings are proportional to the brane cosmological constant. Thus in an era of large cosmological constant these fields have significant role in physical phenomena because of their enhanced couplings with the vis…
We obtain the general inflationary solutions for the slab of five-dimensional AdS spacetime where the fifth dimension is an orbifold $S^1/Z_2$ and two three-branes reside at its boundaries, of which the Randall-Sundrum model corresponds to the static limit. The investigation of the general solutions and their static limit reveals that the RS model recasts both the cosmological constant problem and the gauge hierarchy problem into the balancing problem of the bulk and the brane cosmological constants.
We show that when the antisymmetric Kalb-Ramond field is included in the Randall-Sundrum scenario, although the hierarchy problem can be solved, it requires an extreme fine tuning of the Kalb-Ramond field (about 1 part in $10^{62}$). We interpret this as the return of the problem in disguise. Further, we show that the Kalb-Ramond field induces a small negative cosmological constant on the visible brane.
A mapping between two braneworld cosmologies -- Randall-Sundrum and holographic -- is explicitly constructed. The cosmologies are governed by the appropriate modified Friedman equations. A relationship between the corresponding Hubble rates is established.
In the search for extra dimension through dilepton events in 7-TeV proton-proton collision, the ATLAS detector at LHC has set stringent lower bound on the mass of the Randall-Sundrum (RS) lightest graviton Kaluza-Klein (KK) mode. Considering that the Randall-Sundrum model undertakes to resolve the well-known gauge hierarchy/fine tuning problem to restrict the Higgs mass within the estimated $\sim 126$ GeV against large radiative correction upto the cut-off of the model, we explore the allowed parameter space within which the RS model can be trusted. We show that the consistency of the model wi…
We revive an old result, that one-loop corrections to the graviton propagator induce 1/r^3 corrections to the Newtonian gravitational potential, and compute the coefficient due to closed loops of the U(N) {\cal N}=4 super-Yang-Mills theory that arises in Maldacena's AdS/CFT correspondence. We find exact agreement with the coefficient appearing in the Randall-Sundrum brane-world proposal. This provides more evidence for the complementarity of the two pictures.
Chern-Simons AdS supergravity theories are gauge theories for the super-AdS group. These theories possess a fermionic symmetry which differs from standard supersymmetry. In this paper, we study five-dimensional Chern-Simons AdS supergravity in a Randall-Sundrum scenario with two Minkowski 3-branes. After making modifications to the D = 5 Chern-Simons AdS supergravity action and fermionic symmetry transformations, we obtain a Z_2-invariant total action S = \tilde{S}_bulk + S_brane and fermionic transformations \tildeδ_ε. While \tildeδ_ε\tilde{S}_bulk = 0, the fermionic symmetry is broken by S_b…
A generalized version of the Randall-Sundrum model-2 with different cosmological constants on each side of a brane has been discussed. A possibility of replacing the singular brane by a configuration of a scalar field has been also considered, the Einstein equations for this setup were solved and stability of the solution discussed. It has been shown that under mild assumptions the relation between cosmological constants and the brane tension obtained in the brane limit does not depend on the particular choice of the regularizing profile of the scalar field.
Considering the Randall-Sundrum background, we calculate the total cross-section for $ϕϕ^\star \to G γ$ in the framework of the scalar electrodynamics.
We investigate the semiclassical instability of the Randall-Sundrum brane world. We carefully analyze the bubble solution with the Randall-Sundrum background, which expresses the decay of the brane world. We evaluate the decay probability following the Euclidean path integral approach to quantum gravity. Since a bubble rapidly expands after the nucleation, the entire spacetime will be occupied by such bubbles.
We consider a string-inspired torsion-dilaton-gravity action in a Randall-Sundrum brane world scenario and show that, in an effective four-dimensional theory on the visible brane, the rank-2 antisymmetric Kalb-Ramond field (source of torsion) is exponentially suppressed. The result is similar to our earlier result in [12], where no dilaton was present in the bulk. This offers an explanation of the apparent invisibility of torsion in our space-time. However, in this case the trilinear couplings ~ Tev^{-1} between dilaton and torsion may lead to new signals in Tev scale experiments, bearing the …
We show how the $T^2$ deformation of large $N$, holographic conformal field theories arise from coupling them to the quadratic mass term of ghost-free massive gravity. We then show that in a certain approximation, the equations arising from the variation of the background frame field are those of the Randall--Sundrum II scenario.
We provide the first complete analysis of cosmological evolution in the Randall-Sundrum model with stabilized dilaton. We give the exact expansion law for matter densities on the two branes with arbitrary equations of state. The effective four-dimensional theory leads to standard cosmology at low energy. The limit of validity of the low energy theory and possible deviations from the ordinary expansion law in the high energy regime are finally discussed.
We compute the two-derivative low-energy effective action for the radion in the (supersymmetric) Randall-Sundrum scenario with detuned brane tensions. At the classical level, a potential automatically stabilizes the distance between the branes. In the supersymmetric case, supersymmetry can be broken spontaneously by a vacuum expectation value for the fifth component of the graviphoton.
We present a Randall-Sundrum toy model with an added scalar singlet that couples only to KK fermions in the bulk. Such a scalar would nontrivially affect radion phenomenology. In addition, we examine the radion phenomenology in light of the new scalar and show how this scalar could present another probe to search for the radion.
We discuss the semiclassical instability of the Randall-Sundrum brane-world model against a creation of a kind of Kaluza-Klein bubble. An example describing such a bubble space-time is constructed from the five-dimensional AdS-Schwarzschild metric. The induced geometry of the brane looks like the Einstein-Rosen bridge, which connects the positive and the negative tension branes. The bubble rapidly expands and there also form a trapped region around it.
We investigate the spectroscopy of scalar and vector Kaluza-Klein modes that arise in a deformed Randall-Sundrum model that is constructed from Brans-Dicke theory. The non-minimal coupling in the Brans Dicke theory translates into a deformation of the Randall-Sundrum geometry that depends on the Brans-Dicke parameter $ω$. We find that the $ω$ parameter has a non-trivial effect in the spectroscopy of scalar and vector Kaluza-Klein modes. Our results suggest the interpretation of $ω$ as a fine-tuning parameter.
Unparticle behavior is shown to be realized in the Randall-Sundrum 2 (RS 2) and the Lykken-Randall (LR) brane scenarios when brane-localized Standard Model currents are coupled to a massive vector field living in the five-dimensional warped background of the RS 2 model. By the AdS/CFT dictionary these backgrounds exhibit certain properties of the unparticle CFT at large N_c and strong 't Hooft coupling. Within the RS 2 model we also examine and contrast in detail the scalar and vector position-space correlators at intermediate and large distances. Unitarity of brane-to-brane scattering amplitu…
It is shown that the gravitational redshift as predicted by Einstein's theory, is modified in presence of second rank antisymmetric tensor (Kalb-Ramond) field in a string inspired background spacetime.In presence of extra dimensions, the Randall-Sundrum brane world scenario is found to play a crucial role in suppressing this additional shift. The bound on the value of the warp factor is determined from the redshift data and is found to be in good agreement with that determined from the requirements of Standard model.
By setting some special boundary conditions in the variational principle we obtain junction conditions for the five-dimensional $f(R)$ gravity which in the Einstein limit $f(R)\rightarrow R$ transform into the standard Randall-Sundrum junction conditions. We apply these junction conditions to a particular model of a Friedmann universe on the brane and show explicitly that the limit gives the standard Randall-Sundrum model Friedmann equation.
Recursive relations from diffeomorphism in the Randall-Sundrum model
College of Physics and Communication Electronics, Jiangxi Normal University（江西师范大学物理与通信电子学院）；Laboratoire de Physique Theorique et Hautes Energies, UMR 7589, Sorbonne Université & CNRS（索邦大学与法国国家科学研究中心理论物理与高能物理联合实验室）
We construct the second variation Lagrangian for Randall-Sundrum model with two branes, study its gauge invariance, find the corresponding equations of motion and decouple them. We also derive an effective Lagrangian for this model in the unitary gauge, which describes a massless graviton, massive gravitons and a massless scalar radion. It is shown that the mass spectra of these fields and their couplings to the matter are different on different branes.
We prove the following variational principle for asymptotically Randall-Sundrum (RS) black holes, based on the first law of black hole mechanics: Instantaneously static initial data that extremizes the mass yields a static black hole, for variations at fixed apparent horizon area, AdS curvature length, cosmological constant, brane tensions, and RS brane warp factors. This variational principle is valid with either two branes (RS1) or one brane (RS2), and is applicable to variational trial solutions.
The Kaluza-Klein theory and Randall-Sundrum theory are examined comparatively, with focus on the five dimensional (Dirac) fermion and the dimensional reduction to four dimensions. They are treated in the Cartan formalism. The chiral property, localization, anomaly phenomena are examined. The electric and magnetic dipole moment terms naturally appear. The order estimation of the couplings is done. This is a possible origin of the CP-violation.
Models with one warped and two unwarped extra dimensions allow for the solution of a number of open questions in particle physics. They can be used to solve the hierarchy problem in the same sense as Randall-Sundrum extra dimensions, they incorporate the Randall-Sundrum approach to flavor, and they generate a dark matter candidate via Kaluza-Klein parity in the flat extra dimensions. In this paper, we examine the models AdS_5 x T_2 and AdS_5 x S_2, deriving the Kaluza-Klein spectrum for fermions propagating in the bulk. While the toroidal model allows for a chiral zero mode, we find that the p…
We find renormalization group transformations for the compactified Randall-Sundrum scenario by integrating out an infinitesimal slice of ultraviolet degrees of freedom near the Planck brane. Under these transformations the coefficients of operators on the Planck brane experience RG evolution. The extra-dimensional radius also scales, flowing to zero in the IR. We find an attractive fixed point in the context of a bulk scalar field theory. Calculations are simplified in the low energy effective theory as we demonstrate with the computation of a loop diagram.
We study the problem of integrating an invisible axion into the Randall-Sundrum scenario as an example of how to generate new energy scales between the extremes of the Planck mass and the electroweak scale. In this scenario, the axion corresponds to the phase of complex bulk scalar field. We show how to generate an intermediate energy scale by including a third brane in the scenario. We discuss the stabilization of this brane in detail to demonstrate that no additional fine-tunings arise.
We discuss some issues about the holographic interpretation of the compact Randall-Sundrum model, which is conjectured to be dual to a 4d field theory with non-linearly realized conformal symmetry. We make several checks of this conjecture. In particular, we show that the radion couples conformally to a background 4d metric. We also discuss the interpretation of the Goldberger-Wise mechanism for stabilizing the radion. We consider situations where the electroweak breaking stabilizes the radion and we discuss the issue of natural conservation of flavor quantum numbers.
We study the inflationary dynamics of the universe in the Randall-Sandrum typeII Braneworld model. We consider both an inverse-power law and exponential potentials and apply the Slow-Roll approximation in high energy limit to derive analytical expression of relevant inflationary quantities. An upper bound for the coupling constant was also obtained and a numerical value of perturbation spectrum is calculated in good agreement with observation.
In the Randall-Sundrum scenario, our universe is a 4-dimensional `brane' living in a 5-dimensional bulk spacetime. By studying the scattering of bulk gravity waves, we show that this brane rings with a characteristic set of complex quasinormal frequencies, much like a black hole. To a bulk observer these modes are interpreted as metastable gravity wave bound states, while a brane observer views them as a discrete spectrum of decaying massive gravitons. Potential implications of these scattering resonances are discussed.
It has been proposed that Randall-Sundrum models can be holographically described by a regularized (broken) conformal field theory. We analyze the foundations of this duality using a regularized version of the AdS/CFT correspondence. We compare two- and three-point correlation functions and find the same behaviour in both descriptions. In particular, we show that the regularization of the deformed CFT generates kinetic terms for the sources, which hence can be naturally treated as dynamical fields. We also discuss the counterterms required for two- and three-point correlators in the renormaliz…
A new mechanism which leads to a linearized massless graviton localized on the brane is found in the $AdS$/CFT setting, {\it i.e.} in a single copy of $AdS_5$ spacetime with a singular brane on the boundary, within the Randall-Sundrum brane-world scenario. With an help of a recent development in path-integral techniques, a one-parameter family of propagators for linearized gravity is obtained analytically, in which a parameter $ξ$ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition ($ξ= 0$) the graviton…
We consider a model of a holographic braneworld universe in which a cosmological fluid occupies a 3+1 dimensional brane located at the boundary of the asymptotic AdS$_5$ bulk. We combine the AdS/CFT correspondence and the second Randall-Sundrum (RSII) model to establish a relationship between the RSII braneworld cosmology and the boundary metric induced by the time dependent bulk geometry. In the framework of the Friedmann Robertson Walker cosmology we discuss some physically interesting scenarios involving the RSII and holographic braneworlds.
In the context of the Randall-Sundrum braneworld, the minimal geometric deformation approach (MGD) is used to generate an exact analytic interior solution to four-dimensional effective Einstein's field equations for a spherically symmetric compact distribution. This solution represents the braneworld version of the well known Tolman IV solution in General Relativity. By using this analytic solution, an exhaustive analysis of the braneworld effects on realistic stellar interiors is developed, finding strong evidences in favor of the hypothesis that compactness is reduced due to bulk effects on …
The discrete quantum geometric effects play an important role in dynamical evolution in the loop quantum cosmology. These effects which are significant at the high energies lead to the quadratic energy density modifications to the Friedmann equation, as in the Randall-Sundrum braneworld scenarios but with a negative sign. We investigate the scalar field dynamics in this scenario and show the existence of a phase of super-inflation independent of the inverse scale factor modifications as found earlier. In this regime the scalar field mimics the dynamics of a phantom field and vice versa. We als…
We evaluate the Casimir force between two parallel plates in Randall Sundrum (RS) scenarios extended by q compact dimensions. After giving exact expressions for one extra compact dimension (RS 6D model), we generalize to an arbitrary number of compact dimensions. We present the complete calculation for both two brane scenario (RSI model) and one brane scenario (RSII models) using the method of summing over the modes. We investigate the effects of extra dimensions on the magnitude and sign of the force, and comment on limits for the size and number of the extra dimensions.
We extend Randall-Sundrum dynamics to non-conformal metrics corresponding to non-constant dilaton. We study the appareance of space-time naked singularities and the renormalization group evolution of four-dimensional Newton constant.
We calculate the vacuum expectation value of the stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum model, and discuss the consequences of its local behaviour for the self-consistency of the model. We find that, in general, the stress-energy tensor diverges in the vicinity of the branes. Our main conclusion is that the stress-energy tensor is sufficiently complicated that it has implications for the effective potential, or radion stabilisation, methods that have so far been used.
The transfer matrix method is used to analyze resonances in Randall-Sundrum models. Although it has successfully been used previously by us we provide here a comparison between the numerical and analytical models. To reach this we first find new exact solution for the scalar, gauge, Kalb-Ramond and $q-$form fields. Them we calculate numerically the resonances by the transfer matrix method and compare with the analytical result. For completeness, this is done for models with and without the dilaton coupling. The results show a perfect agreement between the analytical and numerical methods.
A recent work has investigated the possibility that the mass scale for the ultraviolet (UV) brane in the Randall-Sundrum (RS) model is of the order 10^3 TeV. In this so called ``Little Randall-Sundrum'' (LRS) model the bounds on the gauge sector are less severe, permitting a lower Kaluza-Klein scale and cleaner discovery channels. However employing a low UV scale nullifies one major appeal of the RS model; namely the elegant explanation of the hierarchy between the Planck and weak scales. In this work we show that by localizing the gauge, fermion and scalar sector of the LRS model on a five di…
Optical activity of electromagnetic waves in a string inspired Kalb-Ramond cosmological background is studied in presence of extra spacetime dimension. The Kalb-Ramond-electromagnetic coupling which originates from the gauge anomaly cancelling Chern-Simons term in a string inspired model, is explicitly calculated following Randall-Sundrum braneworld conjecture. It is shown that the Randall-Sundrum scenario leads to an enormous enhancement of the optical rotation of a plane polarized electromagnetic wave propagating on the visible brane.Absence of any experimental support in favour of such a la…
In this paper we discuss in detail a numerical method to study resonances in membranes generated by domain walls in Randall-Sundrum-like scenarios. It is based on similar works to understand the quantum mechanics of electrons subject to the potential barriers that exist in heterostructures in semiconductors. This method was used recently to study resonances of a three form field and lately generalized to arbitrary forms. We apply it to a lot of important models, namely those that contain the Gauge, Gravity and Spinor fields. In many cases we find a rich structure of resonances which depends on…
A generalization of the limiting procedure of Penrose, which allows non-zero cosmological constants and takes into account metrics that contain homogeneous functions of degree zero, is presented. It is shown that any spacetime which admits a spacelike conformal Killing vector has a limit which is conformal to plane waves. If the spacetime is an Einstein space, its limit exists only if the cosmological constant is negative or zero. When the conformal Killing vector is hypersurface orthogonal, the limits of Einstein spacetimes are certain AdS plane waves. In this case the nonlinear version of th…
In the context of the Randall-Sundrum braneworld, the minimal geometric deformation approach (MGD) is used to generate a new physically acceptable interior solution to Einstein's field equations for a spherically symmetric compact distribution. This new solution is used to elucidate the role of exterior Weyl stresses from bulk gravitons on compact stellar distributions. We found strong evidences showing that the exterior dark radiation ${\cal U}^+$ always increases both the pressure and the compactness of stellar structures, and that the exterior "dark pressure" ${\cal P}^+$ always reduces the…
We consider the dimensional reduction of a bulk scalar field in the Randall-Sundrum model. By allowing the scalar field to be non-minimally coupled to the spacetime curvature we show that it is possible to generate spontaneous symmetry breaking on the brane.
In the literature about the Randall-Sundrum scenario one finds on one hand that there exist (small) corrections to Newton's law of gravity on the brane, and on another that the exact (and henceforth linearized) Einstein equations can be recovered on the brane. The explanation for these seemingly contradictory results is that the behaviour of the bulk far from the brane is different in both models. We show that explicitely in this paper.
We consider a Randall-Sundrum model in which the Standard Model fermions and gauge bosons correspond to bulk fields. We show how the observed charged fermion masses and CKM mixings can be explained, without introducing hierarchical Yukawa couplings. We then study the impact on the mass scales associated with non-renormalizable operators responsible for proton decay, neutrino masses, and flavor changing neutral currents. Although mass scales as high as 10^{11}- 10^{12} GeV are in principle possible, dimensionless couplings of order 10^{-8} are still needed to adequately suppress proton decay. L…
We study the evolution of scalar perturbations in the radiation-dominated era of Randall-Sundrum braneworld cosmology by numerically solving the coupled bulk and brane master wave equations. We find that density perturbations with wavelengths less than a critical value (set by the bulk curvature length) are amplified during horizon re-entry. Conversely, we explicitly confirm from simulations that the spectrum is identical to GR on large scales. Although this magnification is not relevant for the cosmic microwave background or measurements of large scale structure, it may have some bearing on t…
The generalization of the Randall-Sundrum solution for the warp factor exp[sigma(y)] in the scenario with one extra coordinate y, non-factorizable space-time geometry and two branes isobtained. It is shown that the function obtained sigma(y) is symmetric with respect to an interchange of two branes. It also obeys the orbifold symmetry y -> - y and explicitly reproduces jumps of its derivative on both branes. This solution is defined by the Einstein-Hilbert's equations up to a constant C. It is demonstrated that different values of C results in theories with quite different spectra of the Kaluz…
In this work we have constructed axially symmetric vacuum solutions of the gravitational field equations in a Randall-Sundrum brane. A non-null effective cosmological constant is considered, and asymptotically de Sitter and anti-de Sitter spacetimes are obtained. The solutions describe rotating black holes in a four-dimensional brane. Optical features of the solutions are treated, emphasizing the rotation of the polarization vector along null congruences.
An approach to find the field equation solution of the Randall-Sundrum model with the $S^1/Z_2$ extra axis is presented. We closely examine the infrared singularity. The vacuum is set by the 5 dimensional Higgs field. Both the domain-wall and the anti-domain-wall naturally appear, at the {\it ends} of the extra compact axis, by taking a {\it new infrared regularization}. The stability is guaranteed from the outset by the kink boundary condition. A {\it continuous} (infrared-)regularized solution, which is a truncated {\it Fourier series} of a {\it discontinuous} solution, is utilized.The ultra…
The Gauss-Bonnet interaction is the only consistent quadratic interaction below the Planck scale in the Randall-Sundrum compactification. We study various static and inflationary solutions including this Gauss-Bonnet interaction.
We observe that the main feature of the Randall-Sundrum model, used to solve the hierarchy problem, is already present in a class of Yang-Mills plus gravity theories inspired by noncommutative geometry. Strikingly the same expression for the Higgs potential is found in two models which have no apparent connection. Some speculations concerning the possible relationships are given.
