The general procedure for analyzing the localization of matter fields in Brane models is by integrating, in the action, its zero mode solutions over the extra dimensions. If this is finite, the field is said to be localized. However, the zero mode solutions must also satisfy the Einstein equations. With this in mind, we obtain stringent constraints on a general energy-momentum tensor by analyzing the Einstein's equations. These {\it consistency conditions} must be satisfied for any Braneworld model. We apply it for some fields of the Standard Model. For a free massless scalar field, the zero-mode localization is consistent only if the field does not depend on the extra dimensions. About the spin $\frac{1}{2}$ field with Yukawa-like interactions, we find a very specific relation between Yukawa function and the warp factor. As a consequence, the spinor field localization becomes inconsistent for most of the models studied in the literature. For the free vector field case we find that, independent of the braneworld or the number of extra dimensions, the zero-mode do not satisfy the consistency conditions. Finally, we consider the mechanisms proposed to localize this field. We find that a few survive, and even for these, the consistency conditions fix the free parameters or the possible class of solutions allowed.
Recently, Pal and Skar in [arXiv:hep-th/0701266] proposed a mechanism to arise the warped braneworld models from bulk tachyon matter, which are endowed with a thin brane and a thick brane. In this framework, we investigate localization of fermionic fields on these branes. As in the 1/2 spin case, the field can be localized on both the thin and thick branes with inclusion of scalar background. In the 3/2 spin extension, the general supergravity action coupled to chiral supermultiplets is considered to produce the localization on both the branes as a result.
In this work we study a scenario with a warped 5D smooth braneworld with 4D Minkowski geometry builded from bulk scalar matter non-minimally coupled to gravity with an additional Gauss-Bonnet term. We present exact solutions for the full braneworld configuration in contrast to previous results where only approximate solutions were constructed due to the highly non-linear character of the relevant differential equations. These solutions allow us to study the necessary conditions for the finiteness of the 4D Planck mass and additionally, enables us to perform a more rigorous analysis of 4D gravi…
We propose a brane-world, which contains flavor quarks and mesons, by embedding dimensionally reduced D7-brane in both the supersymmetric and non-supersymmetric 5d background which are obtained as the solutions of type IIB supergravity compactified on Ad$S_5\times S^5$. In the supersymmetric case, the RS brane can be put at any point of the fifth coordinate, but it is pushed to the Ad$S_5$ boundary in the non-supersymmetric case. We study the localization of the flavor mesons, the fluctuation-modes of D7-brane, on the Randall-Sundrum brane in these backgrounds.
In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a localized state to the graviton at zero mode. However, when we consider a double sine-Gordon …
Braneworld models may yield interesting effects ranging from high-energy physics to cosmology, or even some low-energy physics. Their mode structure modifies standard results in these physical realms that can be tested and used to set bounds on the models parameters. Now, to define braneworld deviations from standard 4D physics, a notion of matter and gravity localization on the brane is crucial. In this work we investigate the localization of universal massive scalar fields in a de Sitter thick tachyonic braneworld generated by gravity coupled to a tachyonic bulk scalar field. This braneworld…
Recently, in (Eur.Phys.J.C 80 (2020) 5, 432), the present authors obtained general stringent conditions on the localization of fields in braneworlds by imposing that its zero-mode must satisfy Einstein's equations (EE). Here, we continue this study by considering free $p$-form. These fields present an on-shell equivalency relation between a $p$-form and a $(D-p-2)$-form, provided by Hodge duality (HD). This symmetry will impose a new consistency condition, namely, confinement of a $p$-form must imply the localization of its dual. We apply the above conditions to $6$D braneworlds. With this, we…
It is shown that the consideration of the braneworld consistency conditions within the framework of bulk modified gravities allows for the existence of thick branes in the five- dimensional case with compact extra dimension. In studing the specific consistency conditions in the Brans-Dicke gravity we were able to show that the brane generating scalar field potential is relevant for relaxing the gravitational constraints.
We investigate the localization problem of matter fields within the 5D standing wave braneworld. In this model the brane emits anisotropic waves into the bulk with different amplitudes along different spatial dimensions. We show that in the case of increasing warp factor there exist the pure gravitational localization of all kinds of quantum and classical particles on the brane. For classical particles the anisotropy of the background metric is hidden, brane fields exhibit standard Lorentz symmetry in spite of anisotropic nature of the primordial 5D metric.
We investigate the problem of pure gravitational localization of matter fields within the 5D standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We show that in the case of increasing warp factor there exist normalizable zero modes of spin-0, -1/2, -1, and -2 fields on the brane.
We investigate the problem of localization of gauge fields within the 5D standing wave braneworld model and show that in the case of increasing warp factor there exist normalizable vector field zero modes on the brane.
In this letter we have proposed a natural way of determine the Yukawa coupling $F(z)\barΨΨ$ for the 5D bulk action, the form of the $F(z)$ function allows us to localize the spin--$\frac{1}{2}$ fermionic fields in the paradigm of the 5D braneworld scenarios. The structure acquired by the $V_{L,R}$ potentials is induced by the ansatz for the $F(z)$ function and we show that this choice allows the localization of the left-- or right--chiral KK zero modes $L_{0}(z)$, $R_{0}(z)$ and excludes the tachyonic modes of the KK mass spectrum $m_{L_{n}}$ and $m_{R_{n}}$. The proposal for the function $F(z…
In this paper we investigate the localization and mass spectra of matter fields with spin 0, 1 and 1/2 on a geometric thick brane generated by pure 4D and 5D positive cosmological constants without bulk scalar fields. This model possesses a 4D cosmological constant that can be made as small as one desires without fine-tuning it with the bulk cosmological constant. The RS model is obtained as an analytic continuation of the flat brane limit of this braneworld configuration when the Hubble parameter disappears. Within this inflating braneworld model it is possible to formulate a mechanism for ob…
We introduce new 6D standing wave braneworld model generated by gravity coupled to a phantom-like scalar field and investigate the problem of pure gravitational localization of matter fields. We show that in the case of increasing warp factor spin 0, 1, 1/2 and 2 fields are localized on the brane.
In this work, we propose a standing wave braneworld based on Lyra geometry scenario. The Lyra displacement vector provides a modification in Einstein equations which can be interpreted as a noninteracting phantom scalar. From the Einstein's equation in Lyra manifold, a 5D standing wave braneworld is constructed in the presence of a cosmological constant. Unlike other standing wave solutions presented in the literature, no matter field is necessary to obtain these new solutions. We analyze the properties of the scalar, gauge vector and fermionic fields in this model, highlighting the relevance …
It is known that by introducing the Yukawa coupling between the fermion and the background scalar field, a bulk spin-half fermion can be localized on general Randall-Sundrum braneworlds generated by a kinklike background scalar. However, this localization mechanism does not work anymore for Randall-Sundrum braneworlds generated by a scalar whose configuration is an even function of the extra dimension. In this paper, we present a new localization mechanism for spin-half fermions for such a class of braneworld models, in which extra dimension has the topology $S^1/Z_2$. By two examples, it is s…
Warped braneworld scenario provides an alternative to the usual Kaluza-Klein compactification of extra dimensions through the so-called localization of fields. Randall-Sundrum type models do not directly prove, rather, assume that all standard model fields are localized to the TeV brane. I will provide the mechanism for addressing the problem and discuss the issue of localization of fields on the brane for various types of braneworld models available in the literature.
We investigate scalar and tensor fields in the brane model solution for the 5D space-time with standing gravitational waves in the bulk and show that even in the case of increasing warp factor there exist normalizable zero modes localized on the brane.
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, …
Besides the String Theory context, the quantum General Relativity can be studied by the use of constrained topological field theories. In the celebrated Plebanski formalism, the constraints connecting topological field theories and gravity are imposed in space-times with trivial topology. In the braneworld context there are two distinct regions of the space-time, namely, the bulk and the braneworld volume. In this work we show how to construct topological gravity in a scenario containing one extra dimension and a delta-function like 3-brane which naturally emerges from a spontaneously broken d…
In this paper, we investigate a $6$-dimensional smooth thick braneworld model which contains a compact extra dimension and an infinite large one. The braneworld is generated by a real scalar field with a $ϕ^6$ potential and the bulk is asymptotically $\text{AdS}_6$ spacetime. The geometry achieves the localization of the free $U(1)$ gauge field, which is a problem in the $5$-dimensional Randall-Sundrum-like models. In addition, we analyze the stability of the braneworld system and the localization of gravitons.
In this work, following recent studies which show that it is possible to localize gravity as well as scalar and gauge vector fields in a tachyonic de Sitter thick braneworld, we investigate the localization of fermion fields in this model. In order to achieve this aim we consider the Yukawa interaction term between the fermions and the tachyonic condensate scalar field MF(T)barPsiPsi in the action and analyze four different cases corresponding to distinct tachyonic functions F(T(w)). The only condition that this function must satisfy in order to yield 4D chiral fermions upon dimensional reduct…
Several arguments given in arXiv:1912.12316 suggest that braneworld effective models with fields strictly localized on $δ$-like branes cannot be UV-completed by a fundamental theory including gravity, i.e. they belong to the Swampland. It is concluded that one should instead only consider models with quasilocalized zero-modes of higher-dimensional fields. In this comment, the arguments are critically reviewed, and various loopholes are proposed. Beyond that, the main point that is discussed is the notion of effective brane form factors, which are required when the singular behavior of the bran…
Braneworld theories are often described as low-energy effective field theories (EFTs) featuring an infinitely thin 3-brane and 4D fields exactly localized on it. We investigate whether an exactly localized braneworld can arise as a limit of a theory of 5D fields. Using a holographic formalism we argue that such limit does not exist in the presence of gravity, therefore implying a discontinuity in the space of EFTs. We then present specific models involving exactly localized fields in which inconsistencies appear, which are solved when fields are taken as quasilocalized. Part of our arguments r…
We study a spin 1/2 fermion in a thick braneworld in the context of teleparallel $f(T, B)$ gravity. Here, $f(T,B)$ is such that $f_1(T,B)=T+k_1B^{n_1}$ and $f_2(T,B)=B+k_2T^{n_2}$, where $n_{1,2}$ and $k_{1,2}$ are parameters that control the influence of torsion and the boundary term. We assume Yukawa coupling, where one scalar field is coupled to a Dirac spinor field. We show how the $n_{1,2}$ and $k_{1,2}$ parameters control the width of the massless Kaluza-Klein mode, the breadth of non-normalized massive fermionic modes, and the properties of the analogue quantum-potential near the origin…
We study localization properties of fundamental fields which are coupled to one another through the gauge mechanism both in the original Randall-Sundrum (RS) and in the modified Randall-Sundrum (MRS) braneworld models: scalar-vector, vector-vector, and spinor-vector configuration systems. For this purpose we derive conditions of localization, namely the finiteness of integrals over the extra coordinate in the action of the system considered. We also derive field equations for each of the systems and then obtain their solutions corresponding to the extra dimension by a separation of variable me…
The 6D braneworld with the phantom-like bulk scalar field is considered. We demonstrate pure gravitational localization of scalar field zero modes on the brane.
Localization of a spin-$1/2$ fermion on the braneworld is an important and interesting problem. It is well known that a five-dimensional free massless fermion $Ψ$ minimally coupled to gravity cannot be localized on the Randall-Sundrum braneworld. In order to trap such a fermion, the coupling between the fermion and bulk scalar fields should be introduced. In this paper, localization and quasilocalization of a bulk fermion on the thick braneworld generated by two scalar fields (a kink scalar $ϕ$ and a dilaton scalar $π$) are investigated. Two types of couplings between the fermion and two scala…
We investigate localization problem for gauge fields within the 5D standing wave braneworld with real scalar field and show that there exist normalizable vector field zero modes on the brane.
In a Randall-Sundrum type II inflationary scenario we compute perturbation amplitudes and spectral indices up to next-to-lowest order in the slow-roll parameters, starting from the well-known lowest-order result for a de Sitter brane. Using two different prescriptions for the tensor amplitude, we show that the braneworld consistency equations are not degenerate with respect to the standard relations and we explore their observational consequences. It is then shown that, while the degeneracy between high- and low-energy regimes can come from suitable values of the cosmological observables, exac…
In this work we show that universal gauge vector fields can be localized on the recently proposed 5D thick tachyonic braneworld which involves a de Sitter cosmological background induced on the 3-brane. Namely, by performing a suitable decomposition of the vector field, the resulting 4D effective action corresponds to a massive gauge field, while the profile along the extra dimension obeys a Schroedinger-like equation with a Poeschl-Teller potential. It turns out that the massless zero mode of the gauge field is bound to the expanding 3-brane and allows us to recover the standard 4D electromag…
We show that within tachyonic braneworld models,"super-exponential" warp factors of the form $e^{-2f} \sim e^{-2c_1e^{c_2 |σ|}}$ are problematic when dealing with both the finiteness of the effective four-dimensional (4d) Planck mass and the localization of 4d gravity, which can be stated by the requirement that $\int e^{-2f(σ)}dσ< \infty$, because this condition necessarily implies that c_1 and c_2 should be positive. As a consequence of this fact the tachyonic field $T$ turns out to be complex in contradiction with the real nature of the starting action for the tachyonic braneworld. Converse…
We revisit D-term inflation with the bounds of the cosmic string tension from gravitational wave observations and consider the possible deviation of the spectral index compared with the $Λ$CDM model in light of prerecombination resolutions of the Hubble tension. D-term inflation requires very small coupling constants under these constraints. We show that natural coupling constants ($g=λ=0.1$) can be achieved in the case of D-term inflation on the brane.
The localization of gravity for (5 + 1)-dimensional intersecting thick braneworld models is thoroughly investigated. Departing from preliminary results for five independent proposals, from I to V, gravity is shown to be localized in the brane. In particular, for models from I to III, only the zero modes are analytically determined. On the other hand, for models IV and V, massive modes are all obtained: a finite number of massive states is identified for model IV, while an infinite but discrete number of massive states bounded from below is exhibited by model V. Considering that the discretenes…
We proposed a six dimensional string-like braneworld built from a warped product between a 3-brane and the Hamilton cigar soliton space, the string-cigar braneworld. This transverse manifold is a well-known steady solution of the Ricci flow equation that describes the evolution of a manifold. The resulting bulk is an interior and exterior metric for a thick string. This is a physical and feasible scenario since the source satisfies the dominant energy condition. It is possible to realize the geometric flow as a result of variations of the matter content of the brane, actually, as its tensions.…
In this work we present a simple thick braneworld model that is generated by an intriguing interplay between a 5D cosmological constant with a de Sitter metric induced in the 3-brane without the inclusion of scalar fields. We show that 4D gravity is localized on this brane, provide analytic expressions for the massive Kaluza-Klein (KK) fluctuation modes and also show that the spectrum of metric excitations displays a mass gap. We finally present the corrections to Newton's law due to these massive modes. This model has no naked singularities along the fifth dimension despite the existence of a…
In the Randall-Sundrum scenario, we analyse the dynamics of an AdS5 braneworld when conformal matter fields propagate in five dimensions. We show that conformal fields of weight -4 are associated with stable geometries which describe the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytropic dark energy on a spherically symmetric 3-brane embedded in the compact AdS5 orbifold. We discuss aspects of the radion stability conditions and of the localization of gravity in the vicinity of the brane.
We present a consistent derivation of the recently proposed 5D anisotropic standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We explicitly solve the corresponding junction conditions, a fact that enables us to give a physical interpretation to the anisotropic energy-momentum tensor components on the brane. So matter on the brane represents an oscillating fluid which emits anisotropic waves into the bulk. We also analyze the Sturm-Liouville problem associated to the correct localization condition of the transverse to the brane metric and scalar fields. It is …
In this paper we study fermion localization and resonances on a special type of braneworld model supporting brane splitting. In such models one can construct multi-wall branes which cause considerable simplification in field equations. We use a polynomial superpotential to construct this brane. The suitable Yukawa coupling between the background scalar field and localized fermion is determined. The massive fermion resonance spectrum is obtained. The number of resonances is increased for higher values of Yukawa coupling.
Six dimensional bulk spacetimes with 3-- and 4--branes are constructed using certain non--conventional bulk scalars as sources. In particular, we investigate the consequences of having the phantom (negative kinetic energy) and the Brans--Dicke scalar in the bulk while obtaining such solutions. We find geometries with 4--branes with a compact on--brane dimension (hybrid compactification) which may be assumed to be small in order to realize a 3--brane world. On the other hand, we also construct, with similar sources, bulk spacetimes where a 3--brane is located at a conical singularity. Furthermo…
We consider warped five-dimensional thick braneworlds with four-dimensional Poincaré invariance originated from bulk scalar matter non-minimally coupled to gravity plus a Gauss-Bonnet term. The background field equations as well as the perturbed equations are investigated. A relationship between 4D and 5D Planck masses is studied in general terms. By imposing finiteness of the 4D Planck mass and regularity of the geometry, the localization properties of the tensor modes of the perturbed geometry are analyzed to first order, for a wide class of solutions. In order to explore the gravity localiz…
The localization problem for massive fermions in the 5D standing wave braneworld is considered. The fermion generations on the brane are explained by the existence of three nodes of standing waves in the bulk, where the left and right modes of the 5D fermion are localized and Dirac-type couplings mixes them. We show that in this model the structure of peaks of the left and right fermion wavefunctions in extra dimension leads to the observed mass spectrum of the up and down quark families.
We investigate the dynamics of Randall-Sundrum AdS5 braneworlds with 5-dimensional conformal matter fields. In the scenario with a compact fifth dimension the class of conformal fields with weight -4 is associated with exact 5-dimensional warped geometries which are stable under radion field perturbations and describe on the brane the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytropic dark energy. We analyse the graviton mode flutuations around this class of background solutions and determine their mass eigenvalues and wavefunctions from a Sturm-Liouville pro…
We constructed a six-dimensional version of the standing wave model with an anisotropic 4-brane generated by a phantom-like scalar field. The model represents a braneworld where the compact (on-brane) dimension is assumed to be sufficiently small in order to describe our universe (hybrid compactification). The proposed geometry of the brane and its transverse manifold is non-static, unlike the majority of braneworld models presented in the literature. Furthermore, we have shown that the zero-mode scalar field is localized around the brane. While in the string-like defect the scalar field is lo…
In this manuscript, we discuss the confinement of the spin $\frac{1}{2}$ field on a plethora of branewords models. Recently, in (Eur.Phys.J.C 80 (2020) 5, 432), we studied the consistency of the Standard Model (SM) fields localization on braneworlds with the Einstein equation. In that paper, we discussed the consistency of the spinor field confinement and, by using a Yukawa-like interaction given by $\mathcal{L}_{int}\propto f(y)\barΨΨ$, we obtained that the function must be defined as $f(y)\propto e^{-A}A'$. This shape of the scalar function emerge from the requirement that the spin $\frac{1}…
In this review, we give a brief introduction on the aspects of some extra dimension models and the five-dimensional thick brane models in extended theories of gravity. First, we briefly introduce the Kaluza-Klein theory, the domain wall model, the large extra dimension model, and the warped extra dimension models. Then some thick brane solutions in extended theories of gravity are reviewed. Finally, localization of bulk matter fields on thick branes is discussed.
In this work we analyze the zero mode localization and resonances of $1/2-$spin fermions in co-dimension one Randall-Sundrum braneworld scenarios. We consider delta-like, domain walls and deformed domain walls membranes. Beyond the influence of the spacetime dimension $D$ we also consider three types of couplings: (i) the standard Yukawa coupling with the scalar field and parameter $η_1$, (ii) a Yukawa-dilaton coupling with two parameters $η_2$ and $λ$ and (iii) a dilaton derivative coupling with parameter $h$. Together with the deformation parameter $s$, we end up with five free parameter to …
In this paper we investigate the localization and mass spectra of bulk matter fields on a Gergory-Rubakov-Sibiryakov-inspired braneworld. In this braneworld model, there are one thick brane located at the origin of the extra dimension and two thin branes at two sides. For spin 1/2 fermions coupled with the background scalar $ϕ$ via $η\barΨϕ^pΨ$ with $p$ a positive odd integer, the zero mode of left-hand fermions can be localized on the thick brane for finite distance of the two thin branes, and there exist some massive bound modes and resonance modes. The resonances correspond to the quasi-loc…
We discuss the backreaction of a massless, minimally coupled, quantized scalar field on a thick, two-dimensional de Sitter (dS) brane as an extension of our previous work. We show that a finite brane thickness naturally regularizes the backreaction on the brane. The quantum backreaction exhibits a quadratic divergence in the thin wall limit. We also give a theoretical bound on the brane thickness, in terms of the brane self-consistency of the quantum corrected Einstein equation, namely the requirement that the size of the backreaction should be smaller than that of the background stress-energy…
In this letter we introduce a novel way to spontaneously localize particles (including gauge bosons) and gravitons kinetic terms on a four-dimensional brane via a gravitational mechanism. The model underlying this localization mechanism can be considered as a high-energy resolution of the so-called braneworlds scenario. In particular, we show how to construct a braneworld with induced gravity without pathologies. Finally, we argue that the brane is only stable if its own mass does not exceed a critical value related to the particles-gravity couplings.
Scalar and tensor perturbations arising in an inflationary braneworld scenario driven by a single scalar field are considered, where the bulk on either side of the brane corresponds to Anti-de Sitter spaces with different cosmological constants. A consistency relation between the two spectra is derived and found to have an identical form to that arising in standard single-field inflation based on conventional Einstein gravity. The dS/CFT correspondence may provide further insight into the origin of this degeneracy. Possible ways of lifting such a degeneracy are discussed.
We consider the static domain wall braneworld scenario constructed from the Palatini formalism $f(\mathcal{R})$ theory. We check the self-consistency under scalar perturbations. By using the scalar-tensor formalism we avoid dealing with the higher-order equations. We develop the techniques to deal with the coupled system. We show that under some conditions, the scalar perturbation simply oscillates with time, which guarantees the stability. We also discuss the localization condition of the scalar mode by analyzing the effective potential and the fifth dimensional profile of the scalar mode. We…
We study axially symmetric codimension-2 cosmology for a distributional braneworld fueled by a localised 4D perfect fluid, in a 6D Lovelock theory. We argue that only the matching conditions (dubbed topological) where the extrinsic curvature on the brane has no jump describe a pure codimension-2 brane. If there is discontinuity in the extrinsic curvature on the brane, this induces inevitably codimension-1 distributional terms. We study these topological matching conditions, together with constraints from the bulk equations evaluated at the brane position, for two cases of regularisation of the…
We have investigated the features of the gauge vector field in a braneworld scenario built as a warped product between a 3-brane and a 2-cycle of the resolved conifold. This scenario allowed us to study how the gauge field behaves when the transverse manifold evolves upon a geometric flow that controls the singularity at the origin. Besides, since the transverse manifold has a cylindrical symmetry according to the 3-brane, this geometry can be regarded as a near brane correction of the string-like branes. Indeed, by means of a new warp function and the angular metric component of the resolved …
Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional warped gravity with some matter content, braneworld models must prove to be {\it stable} under the whole set of small fluctuations of the gravitational and matter fields background, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tach…
