Positive Tension Brane Research Articles

Braneworld sum rules and positive tension branes in a massive gravity

By taking advantage of the braneworld sum rules, we explore the feasibility of constructing a flat 3-brane scenario consisting solely of positive tension branes in a 5D extension of the Lorentz-violating massive gravity. It is found that the theory supports three distinct brane configurations, one of which is exactly what we expected, consisting solely of two positive tension branes. The cosmological problem of Randall-Sundrum-1 model and the gauge hierarchy problem can be solved in this model simultaneously. Furthermore, the analysis of linear perturbations reveals that the tensor, vector and scalar modes are all massive and share the same mass spectrum, except that the ground state of vector mode is absent. Moreover, the tensor and vector modes are robust, but the scalar mode is ghost-like. Interestingly, even though the Kaluza-Klein gravitons have an extremely small mass splitting scale, an estimation of the effective gravitational potential and production of these gravitons on the brane indicates that the phenomenology of the present model is equivalent to that of the 6D ADD model.

Localization and mass spectra of various matter fields on Weyl thin brane

It has been shown that the thin brane model in a five-dimensional Weyl gravity can deal with the wrong-signed Friedmann-like equation in the Randall–Sundrum-1 (RS1) model. In the Weyl brane model, there are also two branes with opposite brane tensions, but the four-dimensional graviton (the gravity zero mode) is localized near the negative tension brane, while our four-dimensional universe is localized on the positive tension brane. In this paper, we consider the mass spectra of various bulk matter fields (i.e., scalar, vector, and fermion fields) on the Weyl brane. It is shown that the zero modes of those matter fields can be localized on the positive tension brane under some conditions. The mass spectra of the bulk matter fields are equidistant for the higher excited states, and relatively sparse for the lower excited states. The size of the extra dimension determines the gap of the mass spectra. We also consider the correction to the Newtonian potential in this model and it is proportional to 1/r^{3}.

Stability and binding energy of small asymptotically Randall-Sundrum black holes

We study the binding of a small black hole to a positive-tension brane in the second Randall-Sundrum scenario (RS2) with orbifold symmetry. We find that a small black hole on the brane has substantial gravitational binding energy to the brane, and is stable against escaping into the bulk. This result can be applied in other models with an orbifold-symmetric brane. We also find a novel static black hole, which is completely localized off the brane and is unstable against translations transverse to the brane. Our results are obtained analytically by applying a variational principle to black hole initial data. This paper is the second in a series on asymptotically RS black holes.

Localization and mass spectra of various matter fields on scalar-tensor brane

Recently, a new scalar-tensor braneworld model was presented in [Phys. Rev. D 86 (2012) 127502]. It not only solves the gauge hierarchy problem but also reproduces a correct Friedmann-like equation on the brane. In this new model, there are two different brane solutions, for which the mass spectra of gravity on the brane are the same. In this paper, we investigate localization and mass spectra of various bulk matter fields (i.e., scalar, vector, Kalb-Ramond, and fermion fields) on the brane. It is shown that the zero modes of all the matter fields can be localized on the positive tension brane under some conditions, and the mass spectra of each kind of bulk matter field for the two brane solutions are different except for some special cases, which implies that the two brane solutions are not physically equivalent. When the coupling constants between the dilaton and bulk matter fields take special values, the mass spectra for both solutions are the same, and the scalar and vector zero modes are localized on the negative tension brane, while the KR zero mode is still localized on the positive tension brane.

Cosmological tests of coupled Galileons

We investigate the cosmological properties of Galileon models which admit Minkowski space as a stable solution in vacuum. This is motivated by stable, positive tension brane world constructions that give rise to Galileons. We include both conformal and disformal couplings to matter and focus on constraints on the theory that arise because of these couplings. The disformal coupling to baryonic matter is extremely constrained by astrophysical and particle physics effects. The disformal coupling to photons induces a cosmological variation of the speed of light and therefore distorsions of the Cosmic Microwave Background spectrum which are known to be very small. The conformal coupling to baryons leads to a variation of particle masses since Big Bang Nucleosynthesis which is also tightly constrained. We consider the background cosmology of Galileon models coupled to Cold Dark Matter (CDM), photons and baryons and impose that the speed of light and particle masses respect the observational bounds on cosmological time scales. We find that requiring that the equation of state for the Galileon models must be close to -1 now restricts severely their parameter space and can only be achieved with a combination of the conformal and disformal couplings. This leads to large variations of particle masses and the speed of light which are not compatible with observations. As a result, we find that cosmological Galileon models are viable dark energy theories coupled to dark matter but their couplings, both disformal and conformal, to baryons and photons must be heavily suppressed making them only sensitive to CDM.

Pure geometric branes and mass hierarchy

We consider a toy model with flat thin branes embedded in a five-dimensional Weyl integrable manifold, where the geometric Weyl scalar provides the material that constitute the brane configurations. The brane configuration is similar to the Randall–Sundrum model. However, it is found that the massless graviton is localized on the brane with negative tension. So, in order to solve the gauge hierarchy problem, our world should be confined on the positive tension brane, and this is crucial to reproduce a correct Friedmann-like equation on the brane. The spacings of graviton mass spectrum are very tiny, but these massive gravitons are hidden in low energy experiments because they are weakly coupled with matter on the brane.

Braneworld teleparallel gravity

We study the gravity in the context of a braneworld teleparallel scenario. The geometrical setup is assumed to be Randall–Sundrum II model where a single positive tension brane is embedded in an infinite AdS bulk. We derive the equivalent of the Gauss–Codacci equations in teleparallel gravity and junction conditions in this setup. Using these results we derive the induced teleparallel field equations on the brane. We show that compared to general relativity, the induced field equations in teleparallel gravity contain two extra terms arising from the extra degrees of freedom in the teleparallel Lagrangian. The term carrying the effects of the bulk to the brane is also calculated and its implications are discussed.

Brane modeling in warped extra-dimension

Abstract Five-dimensional scenarios with infinitesimally thin branes replaced by appropriate configurations of a scalar field were considered. A possibility of periodic extra dimension was discussed in the presence on non-minimal scalar-gravity coupling and a generalized Gibbons-Kallosh-Linde sum rule was found. In order to avoid constraints imposed by periodicity, a non-compact spacial extra dimension was introduced. A five dimensional model with warped geometry and two thin branes mimicked by a scalar profile was constructed and discussed. In the thin brane limit the model corresponds to a set-up with two positive-tension branes. The presence of two branes allows to address the issue of the hierarchy problem which could be solved by the standard warping of the four dimensional metric provided the Higgs field is properly localized. Stability of the background solution was discussed and verified in the presence of the most general perturbations of the metric and the scalar field.

Gravity localization and mass hierarchy in scalar-tensor branes

We consider a braneworld model in the scalar-tensor gravity. In order to solve the gauge hierarchy problem in this model, our world should be confined on the positive tension brane rather than on the negative one. This is crucial to reproduce a correct Friedmann-like equation on the brane. Interestingly, it is found that the spacing of mass spectrum in this scenario is very tiny, but the light gravitons cannot be observed individually in colliders because of their sufficiently weak interaction with matter fields on the visible brane.

Technically natural cosmological constant from supersymmetric 6D brane backreaction

Abstract We provide an explicit example of a higher-dimensional model describing a non-supersymmetric spectrum of 4D particles of mass M, whose 4D geometry – including loop effects – has a curvature that is of order R ∼ m K K 4 / M p 2 , where m K K is the extra-dimensional Kaluza–Klein scale and Mp is the 4D Planck constant. m K K is stabilized and can in particular satisfy m K K ≪ M . The system consists of a (5+1)-dimensional model with a flux-stabilized supersymmetric bulk coupled to non-supersymmetric matter localized on a (3+1)-dimensional positive-tension brane. We use recent techniques for calculating how extra dimensions respond to changes in brane properties to show (at the classical level) that the extra-dimensional volume adjusts to ensure that the low-energy 4D geometry is exactly flat, independent of the value of the brane tensions. Its mechanism for doing so is the transfer of stabilizing flux between the bulk and the branes. The UV completion of the model can arise at scales much larger than M, allowing the calculation of quantum effects like the zero-point energy of very massive particles in the vacuum. We find that brane-localized loops do not affect the 4D curvature at all, but bulk loops can. These can be estimated on general grounds and we show that supersymmetry dictates that they generate curvatures that are generically of order m K K 4 / M p 2 . For realistic applications this points to a world with two supersymmetric extra dimensions, with supersymmetry in the bulk broken at the sub-eV KK scale – as proposed in hep-th/0304256 – requiring a 6D gravity scale somewhat higher than 10 TeV. Ordinary Standard Model particles are brane-localized and not at all supersymmetric (implying in particular no superpartners or the MSSM). We discuss how the model evades various no-go theorems that would naively exclude it, and briefly outline several striking observational implications for tests of gravity and at the LHC.

Bulk axions, brane back-reaction and fluxes

Extra-dimensional models can involve bulk pseudo-Goldstone bosons (pGBs) whose shift symmetry is explicitly broken only by physics localized on branes. Reliable calculation of their low-energy potential is often difficult because it requires an understanding of the dynamics that stabilizes the geometry of the extra dimensions. Rugby ball solutions provide simple examples of extra-dimensional configurations for which two compact extra dimensions are stabilized in the presence of only positive-tension brane sources. The effects of brane back-reaction can be computed explicitly for these systems, allowing the calculation of the shape of the low-energy pGB potential, V 4D (φ), as a function of the perturbing brane properties, as well as the response of both the extra dimensional and on-brane geometries to this stabilization. If the φ-dependence is a small part of the total brane tension a very general analysis is possible, permitting an exploration of how the system responds to frustration when the two branes disagree on what the proper scalar vacuum should be. We show how the low-energy potential is given by the sum of brane tensions (in agreement with common lore) when only the brane tensions couple to φ. We also show how a direct brane coupling to the flux stabilizing the extra dimensions corrects this result in a way that does not simply amount to the contribution of the flux to the brane tensions. The mass of the low-energy pseudo-Goldstone mode is of order m a ∼ (μ/F)2 m KK (where μ is the energy scale associated with the brane symmetry breaking and F < M p is the extra-dimensional axion decay constant). In principle this can be larger or smaller than the Kaluza-Klein scale, m KK, but when it is larger axion properties cannot be computed purely within a 4D approximation (as they usually are). We briefly describe several potential applications, including a brane realization of ‘natural inflation,’ and a dynamical mechanism for suppressing the couplings of the pGB to matter localized on the branes. Since the scalar can be light enough to be relevant to precision tests of gravity (in a technically natural way) this mechanism can be relevant to evading phenomenological bounds.

Codimension-2 brane–bulk matching: examples from six and ten dimensions

Experience with Randall–Sundrum models teaches the importance of following how branes back-react onto the bulk geometry, since this can dramatically affect the system's low-energy properties. Yet the practical use of this observation for model building is so far mostly restricted to branes having only one transverse dimension (codimension-1) in the bulk space, since this is where tools for following back-reaction are well developed. This is likely to be a serious limitation since experience also tells us that one dimension is rarely representative of what happens in higher dimensions. Here we summarize recent progress in developing the matching conditions that describe how codimension-2 branes couple to bulk metric, gauge and scalar fields. These matching conditions are then applied to three situations: D7-branes in F-theory compactifications of ten-dimensional (10D) Type IIB string vacua; 3-branes coupled to bulk axions in unwarped and non-supersymmetric six-dimensional (6D) systems; and 3-branes coupled to chiral, gauged 6D supergravity. For each it is shown how the resulting brane–bulk dynamics are reproduced by the scalar potential for the low-energy moduli in the dimensionally reduced, on-brane effective theory. For 6D supergravity, we show that the only 4D-maximally symmetric bulk geometries supported by positive-tension branes are flat.

General perturbations for braneworld compactifications and the six dimensional case

Our main objective is to study how braneworld models of higher codimension differ from the 5D case and traditional Kaluza-Klein compactifications. We first derive the classical dynamics describing the physical fluctuations in a wide class of models incorporating gravity, non-Abelian gauge fields, the dilaton and two-form potential, as well as 3-brane sources. Next, we use these results to study braneworld compactifications in 6D supergravity, focusing on the bosonic fields in the minimal model; composed of the supergravity-tensor multiplet and the U(1) gauge multiplet whose flux supports the compactification. For unwarped models sourced by positive tension branes, a harmonic analysis allows us to solve the large, coupled, differential system completely and obtain the full 4D spin-2,1 and 0 particle spectra, establishing (marginal) stability and a qualitative behaviour similar to the smooth sphere compactification. We also find interesting results for models with negative tension branes; extra massless Kaluza-Klein vector fields can appear in the spectra, beyond those expected from the isometries in the internal space. These fields imply an enhanced gauge symmetry in the low energy 4D effective theory obtained by truncating to the massless sector, which is explicitly broken as higher modes are excited, until the full 6D symmetries are restored far above the Kaluza-Klein scale. Remarkably, the low energy effective theory does not seem to distinguish between a compactification on a smooth sphere and these singular, deformed spheres.

GHOSTS AND TACHYONS IN THE FIFTH DIMENSION

We present several solutions for the five-dimensional gravity models in the presence of bulk ghosts and tachyons to argue that these "troublesome" fields can be a useful model-building tool. The ghost-like signature of the kinetic term for a bulk scalar creates a minimum in the scale factor, removing the necessity for a negative tension brane in models with the compactified fifth dimension. It is shown that the model with the positive tension branes and a ghost field in the bulk leads to the radion stabilization. The bulk scalar with the variable sign kinetic term can be used to model both positive and negative tension branes of a finite width in the compact dimension. Finally, we present several ghost and tachyon field configurations in the bulk that lead to the localization of gravity in four dimensions, including one solution with the Gaussian profile for the metric, gμν(y) = ημν exp {-αy2}, which leads to a stronger localization of gravity than the Randall–Sundrum model.

Synergistic gravity and the role of resonances in GRS-inspired braneworlds

We consider 5D braneworld models of quasi-localized gravity in which 4D gravity is reproduced at intermediate scales while the extra dimension opens up at both the very short and the very long distances, where the geometry is flat. Our main interest is the interplay between the zero mode of these models, whenever a normalizable zero mode exists, and the effects of zero energy graviton resonant modes coming from the contributions of massive KK modes. We first consider a compactified version of the GRS model and find that quasi-localized gravity is characterized by a scale for which both the resonance and the zero mode have significant contribution to 4D gravity. Above this scale, gravity is primarily mediated by the zero mode, while the resonance gives only minor corrections. Next, we consider an asymmetric version of the standard non-compact GRS model, characterized by different cosmological constants on each AdS side. We show that a resonance is present but the asymmetry, through the form of the localizing potential, can weaken it, resulting in a shorter lifetime and, thus, in a shorter distance scale for 4D gravity. As a third model exhibiting quasi-localization, we consider a version of the GRS model in which the central positive tension brane has been replaced by a configuration of a scalar field propagating in the bulk.

Stability and negative tensions in 6D brane worlds

We investigate the dynamical stability of warped, axially symmetric compactifications in anomaly free 6D gauged supergravity. The solutions have conical defects, which we source by 3-branes placed on orbifold fixed points, and a smooth limit to the classic sphere-monopole compactification. Like for the sphere, the extra fields that are generically required by anomaly freedom are especially relevant for stability. With positive tension branes only, there is a strict stability criterion (identical to the sphere case) on the charges present under the monopole background. Thus brane world models with positive tensions can be embedded into anomaly free theories in only a few ways. Meanwhile, surprisingly, in the presence of a negative tension brane the stability criteria can be relaxed. We also describe in detail the geometries induced by negative tension codimension two branes.

Solution of a braneworld big crunch/big bang cosmology

We solve for the cosmological perturbations in a five-dimensional background consisting of two separating or colliding boundary branes, as an expansion in the collision speed V divided by the speed of light c. Our solution permits a detailed check of the validity of four-dimensional effective theory in the vicinity of the event corresponding to the big crunch/big bang singularity. We show that the four-dimensional description fails at the first nontrivial order in (V/c){sup 2}. At this order, there is nontrivial mixing of the two relevant four-dimensional perturbation modes (the growing and decaying modes) as the boundary branes move from the narrowly separated limit described by Kaluza-Klein theory to the well-separated limit where gravity is confined to the positive-tension brane. We comment on the cosmological significance of the result and compute other quantities of interest in five-dimensional cosmological scenarios.

On Newton's law in supersymmetric braneworld models

We study the propagation of gravitons within 5-D supersymmetric braneworld models with a bulk scalar field. The setup considered here consists of a 5-D bulk spacetime bounded by two 4-D branes localized at the fixed points of an $S^1/Z_2$ orbifold. There is a scalar field $\phi$ in the bulk which, provided a superpotential $W(\phi)$, determines the warped geometry of the 5-D spacetime. This type of scenario is common in string theory, where the bulk scalar field $\phi$ is related to the volume of small compact extra dimensions. We show that, after the moduli are stabilized by supersymmetry breaking terms localized on the branes, the only relevant degrees of freedom in the bulk consist of a 5-D massive spectrum of gravitons. Then we analyze the gravitational interaction between massive bodies localized at the positive tension brane mediated by these bulk gravitons. It is shown that the Newtonian potential describing this interaction picks up a non-trivial contribution at short distances that depends on the shape of the superpotential $W(\phi)$. We compute this contribution for dilatonic braneworld scenarios $W(\phi) = e^{\alpha \phi}$ (where $\alpha$ is a constant) and discuss the particular case of 5-D Heterotic M-theory: It is argued that a specific footprint at micron scales could be observable in the near future.

DILATON BRANE COSMOLOGY WITH SECOND ORDER STRING CORRECTIONS AND THE COSMOLOGICAL CONSTANT

We consider, in five dimensions, the effective action from heterotic string which includes quantum gravity corrections up to (α′)2. The expansion, in the string frame, is in terms of |α′R|, where R is the scalar curvature and uses the third order Euler density, next to the Gauss–Bonnet term. For a positive tension brane and infinite extra dimension, the logarithmic class of solutions is less dependent from fine-tuning than in previous formulations. More importantly, the model suggests that in the full nonperturbative formulation, the string scale can be much lower than the effective Planck mass, without the string coupling to be vanishingly small. Also, a less severe fine-tuning of the brane tension is needed.

Energy scales in a stabilized brane world

Brane world gravity looks different for observers on positive and negative tension branes. First we consider the well-known RS1 model with two branes embedded into the AdS 5 space–time and recall the results on the relations between the energy scales for an observer on the negative tension brane, which is supposed to be “our” brane. Then from the point of view of this observer we study energy scales and masses for the radion and graviton excitations in a stabilized brane world model. We argue that there may be several possibilities leading to scales of the order 1–10 TeV or even less for new physics effects on our brane. In particular, an interesting scenario can arise in the case of a “symmetric” brane world with a nontrivial warp factor in the bulk, which however takes equal values on both branes.