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 dimensional slice of a doubly warped spacetime one may obtain the low UV brane scale employed in the LRS model and motivate the weak-Planck hierarchy. We also consider the generalization to an n-warped spacetime.
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 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 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…
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.
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 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 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.
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…
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.
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…
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…
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…
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…
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.
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.
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.
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.
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 consider a generalised two brane Randall-Sundrum model with non-zero cosmological constant on the visible TeV brane. Massive Kaluza-Klein modes for various bulk fields namely graviton, gauge field and antisymmetric second rank Kalb-Ramond field in a such generalized Randall-Sundrum scenario are determined. The masses for the Kaluza-Klein excitations of different bulk fields are found to depend on the brane cosmological constant indicating interesting consequences in warped brane particle phenomenology
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…
In Randall-Sundrum two D-brane system we derive the gravitational theory on the branes. It is turned out from the consistency that one D-brane has the negative tension brane under Randall-Sundrum tuning and both gauge fields on the brane are related by scale transformation through the bulk RR/NS-NS fields. As same with the single D-brane case, the gauge field which is supposed to be localised on the brane does not couple to the gravity on the branes.
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 define the 7D Randall-Sundrum (RS) background and construct the corresponding 6D theory via AdS/CFT duality. In simple approximations, the Friedmann equation derived from 7D RS cosmology and the brane view-point results exactly match. Possible cosmologies on the bulk side are also outlined.
The effect of temperature is investigated in the Randall-Sundrum brane-world scenario. It is shown that for a spacetime ansatz motivated by similarity with AdS/CFT correspondence several features of the model, such as its $Z_2$ symmetry, are not maintained at nonzero temperatures.
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.
We address the behaviour of the scalar field with negative mass squared in the five dimensional AdS space where the Randall-Sundrum brane-world is embedded. We point out that the tachyonic scalar allowed in the bulk space destabilizes the embedded brane-world where the cosmological constant is zero. The resolution of this instability is discussed from the viewpoint of AdS/CFT correspondence.
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.
We point out that the gravitational evolution equations in the Randall-Sundrum model appear in a different form than hitherto assumed. As a consequence, the model yields a correct Newtonian limit in a novel manner.
We clarify a mechanism to obtain a massless gauge boson from the Kaluza-Klein approach of the Randall-Sundrum(RS) brane world. This corresponds exactly to the same mechanism of achieving a localization of the gauge boson by adding both the bulk and brane mass terms. Accordingly this work puts another example for a localization-mechanism of the gauge boson on the brane.
The effective action of the radion in the Randall-Sundrum model is analysed. Fine tunings are needed to obtain the observed mass hierarchy and an invisible radion. since the kinetic terms are important for determining the radion mass, the finite quantum corrections from massless conformally coupled fermions are analysed and found to vanish at one loop order.
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.
We numerically construct large Randall-Sundrum II brane black holes in 4 and 5 dimensions from associated AdS/CFT spacetimes. Our solutions are leading order perturbations of a representative of the boundary conformal structure of the AdS spacetime sourced by the dual CFT stress tensor. The 4-dimensional solutions are static perturbations of the Euclidean Schwarzschild metric, while the 5-dimensional solutions are perturbations of the Myers-Perry metric with equal angular momenta. We compare the former with previous numerical results for Randall-Sundrum bulk black holes and find good agreement…
We show the (already known) fact that Randall-Sundrum scenarious although compatible with a ${\mathbb{Z}}_2$ orbifold symmetry cannot hold regularity of the fields at the orbifold planes in the absence of boundary actions and respective jumps of the fields. This makes the models mathematical inconsistence and invalidate the inclusion of such models in a higher dimensional theory such as string theory. For completeness we point out some directions already in the literature and in progress.
The quantisation of a scalar field in the five-dimensional model suggested by Randall and Sundrum is considered. Using the Kaluza-Klein reduction of the scalar field, discussed by Goldberger and Wise, we sum the infinite tower of modes to find the vacuum energy density. Dimensional regularisation is used and we compute the pole term needed for renormalisation, as well as the finite part of the energy density. Some comments are made concerning the possible self-consistent determination of the radius.
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 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.
In the context of an inflationary Randall-Sundrum Type II braneworld (RS2) we calculate spectral indices and amplitudes of cosmological scalar and tensor perturbations, up to second order in slow-roll parameters. Under very simple assumptions, extrapolating next-order formulae from first-order calculations in the case of a de Sitter brane, we see that the degeneracy between standard and braneworld lowest-order consistency equations is broken, thus giving different signatures of early-universe inflationary expansion. Using the latest results from WMAP for estimates of cosmological observables, …
We show that the Gauss-Bonnet term is the only consistent curvature squared interaction in the Randall-Sundrum model and various static and inflationary solutions can be found. And from metric perturbations around the RS background with a single brane embedded, we also show that for a vanishing Gauss-Bonnet coefficient, the brane bending allows us to reproduce the 4D Einstein gravity at the linearized level.
We study a mechanism, inspired from the mechanism for generating the gauge hierarchy in Randall-Sundrum model, to investigate the cosmological constant problem. First we analyze the bulk cosmological constant and brane vacuum energies in RS model. We show that the five-dimensional bulk cosmological constant and the vacuum energies of the two branes all obtain their natural values. Finally we argue how we can generate a small four-dimensional effective cosmological constant on the branes through modifying the original RS model.
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 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 propose another method to compute the Casimir force in noncommutative Randall-Sundrum braneworld model considered by K. Nouicer and Y. Sabri recently. Our method can be used to compute the Casimir force to any order in the noncommutative parameter. Contrary to the claim made by K. Nouicer and Y. Sabri that repulsive Casimir force can appear in the first order approximation, we show that the Casimir force is always attractive at any order of approximation.
Using a fixed-energy amplitude in Randall-Sundrum single brane scenario, we compute the Newton potential on the brane. It is shown that the correction terms to the Newton potential involve a logarithmic factor. Especially, when the distance between two point masses are very small compared to $AdS$ radius, the contribution of KK spectrum becomes dominant compared to the usual inversely square law. This fact may be used to prove the existence of an extra dimension experimentally.
We provide the exact time-dependent cosmological solutions in the Randall-Sundrum (RS) setup with bulk matter, which may be smoothly connected to the static RS metric. In the static limit of the extra dimension, the solutions are reduced to the standard Friedmann equations. In view of our solutions, we also propose an explanation for how the extra dimension is stabilized in spite of a flat modulus potential at the classical level.
The stability problem of Randall-Sundrum braneworld is readdressed in the light of stabilizing bulk scalar fields. It is shown that in such scenario the instability persists because of back-reaction even when an arbitrary potential is introduced for a canonical scalar field in the bulk. It is further shown that a bulk scalar field can indeed stabilize the braneworld when it has a tachyon-like action. The full back-reacted metric in such model is derived and a proper resolution of the hierarchy problem (for which the Randall Sundrum scenario was originally proposed) is found to exist by suitabl…
