Thin Brane Research Articles

Localization of scalar matter with nonminimal derivative coupling on braneworlds

The localization of scalar matter with nonminimal derivative coupling (NMDC) in the braneworld model is studied. Two types of brane models are considered: a thin brane (the Modified Randall-Sundrum) and a thick brane generated by the bulk scalar field. The 5-dimensional theory of scalar field with NMDC is reduced to the effective 4-dimensional theory by imposing the fulfillment of localization conditions. In this article, the localization properties of field with NMDC are examined in both models. We found that the massless and massive scalar field with NMDC can be localized on the MRS thin brane. In the thick brane, the massless scalar field is localized.

The physics of intersecting thick to thin branes

We model four-dimensional junctions made out of intersections of co-dimension one brane living in higher-dimensional spacetimes through domain walls. We take a new look at the problem of localizing fermion states on brane junctions as a result of intersecting one thick brane to others sufficiently thin. All the branes intersect orthogonally to form a four-dimensional junction embedded in a higher-dimensional bulk. We discuss the effects of the Yukawa coupling and the proton decay on the restriction of the parameters that control the junction stability and the brane thickness which also define the bulk cosmological constant.

Sailing past the End of the World and discovering the Island

Large black holes in anti-de Sitter space have positive specific heat and do not evaporate. In order to mimic the behavior of evaporating black holes, one may couple the system to an external bath. In this paper we explore a rich family of such models, namely ones obtained by coupling two holographic CFTs along a shared interface (ICFTs). We focus on the limit where the bulk solution is characterized by a thin brane separating the two individual duals. These systems may be interpreted in a double holographic way, where one integrates out the bath and ends up with a lower-dimensional gravitational braneworld dual to the interface degrees of freedom. Our setup has the advantage that all observables can be defined and calculated by only relying on standard rules of AdS/CFT. We exploit this to establish a number of general results, relying on a detailed analysis of the geodesics in the bulk. Firstly, we prove that the entropy of Hawking radiation in the braneworld is obtained by extremizing the generalized entropy, and moreover that at late times a so-called `island saddle' gives the dominant contribution. We also derive Takayanagi's prescription for calculating entanglement entropies in BCFTs as a limit of our ICFT results.

The extension method for Bloch branes

The nature of gravity and its strength compared with other forces are fundamental challenges faced by the actual science. A path to understand the hierarchy problem of gravity consists in adding an extra dimension to Einstein–Hilbert’s general relativity. Therefore, gravity would be the only force leaking through this region of space–time also known as brane. Despite the success of the mathematical description for the hierarchy issue through simple thin branes, it is also possible to derive a consistent theory of gravity using thick branes. This work unveils a new procedure to determine analytic hybrid thick braneworld models. The discussions were based on the so-called Bloch branes, which are constructed via a two-field model coupled with gravity in five-dimensional space–time. Both fields used to build the Bloch branes depend only on the extra dimension, and the hybrid branes present internal structure, characterizing them as thick. In this work, we were able to derive new analytic thick brane models by using the extension method. Some of these new branes present a Minkowski space–time immersed inside of the fifth dimension. We showed how the symmetry of the emergent branes can be controlled via specific parameters. We also analyzed the stability conditions for each braneworld family, showing possible stable states for gravitons.

Localization of scalar field on f(R, T) thick Robertson-Walker brane

The braneworld model provides a solution to the hierarchy problem in cosmology. Based on its thickness, braneworld models are classified into a thin brane model (RandallSundrum (RS) and the RS-like models) and a thick brane model. The thin brane model has a problem according to the zero-width brane and some fields localization. Meanwhile, thick brane is quite good in explaining fields localization and there is no problem related to brane thickness. In this article, we re-examine the thick brane in a modified gravity, that is f(R,T) gravity. The equation of motion for the y-dependence scalar field and the f(R,T) field equation for a conformally flat brane and Robertson-Walker brane are derived. We also investigate the localization of scalar field on the f(R,T) thick brane, for a specific f(R,T) form. As the results, the formulation of Robertson-Walker thick brane is obtained. It can be reduced and has similarities to the previous f(R,T) brane consideration. It has a possibility to trap the field ϕ(y) in a thick brane with specific conditions of brane’s scale factor. It was shown that the expanding or contracting universe affects the localization conditions of the scalar fields.

Fat brane, dark matter and localized kinetic terms in six dimensions

Extra dimensions (ED) have been used as attempts to explain several phenomena in particle physics over the years. In this paper we investigate the role of an abelian gauge field as mediator of the interaction between dark matter (DM) and Standard Model (SM) particles, in a model with two flat and transverse ED compactified on the chiral square. DM is confined in a thin brane, localized at the origin of the chiral square, while the SM is localized in a finite width brane, lying in the opposite corner of the square. A brane-localized kinetic term is present in the DM brane, while in the fat brane it is not allowed. In this model the kinetic mixing is not required because we assume that the SM particles couple to the mediator through their B-L charges, while DM couples to it via a dark charge. Assuming a complex scalar field as DM candidate it is possible to obtain the observed DM relic abundance and avoid direct detection constraints for some parameter choices.

Gauge field and brane-localized kinetic terms on the chiral square

Extra dimensions have been used as attempts to explain several phenomena in particle physics. In this paper we investigate the role of brane-localized kinetic terms (BLKT) on thin and thick branes with two flat extra dimensions (ED) compactified on the chiral square, and an abelian gauge field in the bulk. The results for a thin brane have resemblance with the 5-D case, leading to a tower of massive KK particles whose masses depend upon the compactification radius and the BLKT parameter. On the other hand, for the thick brane scenario, there is no solution that satisfy the boundary conditions. Because of this, the mechanism of suppressed couplings due to ED (Landim and Rizzo, in JHEP 06:112, 2019) cannot be extended to 6-D.

Thick branes in extra dimensions and suppressed dark couplings

The nature of dark matter (DM) and how it may interact with the various fields of the Standard Model (SM) remains a mystery. In this paper we show that the interaction between new light dark matter mediators and the SM particles can be naturally suppressed if one employs a single, flat extra dimension (ED). In this setup, the SM fields are localized in a finite width ‘fat’ brane, similar to models of Universal Extra Dimensions (UED), while DM, in turn, is confined to a thin brane at the opposite end of the ED interval. Including brane localized kinetic terms on the fat brane for the mediator fields, the resulting coupling between the SM and these light mediators can be several orders of magnitude smaller than the corresponding ones between the mediators and DM which we assume to be a typical gauge coupling. We investigate the implications of this scenario for both vector (i.e, dark photon, DP) and scalar mediator fields in the 5-D bulk. In this setup kinetic mixing, which is usually employed to suppress light mediator couplings, is not required. Here we assume that the SM particles couple to the DP via their B − L charges while the DP couples to the DM via a dark charge. Both the vector DP couplings and the corresponding Higgs portal couplings with the SM are shown to be natural small in magnitude with a size dependent on ratio of the 5-D compactification radius, R−1 ∼ 0.1-1 GeV, and the SM brane thickness, L−1 ∼ 2-10 TeV, a range chosen to avoid LHC and other experimental constraints. In this framework one can obtain the observed value of the DM relic abundance for a wide range of parameter choices, while the constrains due to direct DM detection and the invisible width of the Higgs do not impose significant challenges to the model. Finally, this mechanism can lead to distinct signatures in both present and upcoming experiments as it combines some common features of UED and DP models in a single ED setup.

Holographic complexity for defects distinguishes action from volume

We explore the two holographic complexity proposals for the case of a 2d boundary CFT with a conformal defect. We focus on a Randall-Sundrum type model of a thin AdS2 brane embedded in AdS3. We find that, using the “complexity=volume” proposal, the presence of the defect generates a logarithmic divergence in the complexity of the full boundary state with a coefficient which is related to the central charge and to the boundary entropy. For the “complexity=action” proposal we find that the logarithmically divergent term in the complexity is not influenced by the presence of the defect. This is the first case in which the results of the two holographic proposals differ so dramatically. We consider also the complexity of the reduced density matrix for subregions enclosing the defect. We explore two bosonic field theory models which include two defects on opposite sides of a periodic domain. We point out that for a compact boson, current free field theory definitions of the complexity would have to be generalized to account for the effect of zero-modes.

Nonlinear stability of a brane wormhole

We analytically study the non-linear stability of a spherically symmetric wormhole supported by an infinitesimally thin brane of negative tension, which has been devised by Barcelo and Visser. We consider a situation in which a thin spherical shell composed of dust falls into an initially static wormhole; The dust shell plays a role of the non-linear disturbance. The self-gravity of the falling dust shell is completely taken into account through Israel's formalism of the metric junction. When the dust shell goes through the wormhole, it necessarily collides with the brane supporting the wormhole. We assume the interaction between these shells is only gravity and show the condition under which the wormhole stably persists after the dust shell goes through it.

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}.

Spectrum in the presence of brane-localized mass on torus extra dimensions

The lightest mass eigenvalue of a six-dimensional theory compactified on a torus is numerically evaluated in the presence of the brane-localized mass term. The dependence on the cutoff scale $\Lambda$ is non-negligible even when $\Lambda$ is two orders of magnitude above the compactification scale, which indicates that the mass eigenvalue is sensitive to the size of the brane, in contrast to five-dimensional theories. We obtain an approximate expression of the lightest mass in the thin brane limit, which well fits the numerical calculations, and clarifies its dependence on the torus moduli parameter $\tau$. We find that the lightest mass is typically much lighter than the compactification scale by an order of magnitude even in the limit of a large brane mass.

De Sitter thin brane model

We discuss the large mass hierarchy problem in a braneworld model which represents our acceleratively expanding universe. The Randall-Sundrum (RS) model with warped one extra dimension added to flat 4-dimensional space-time cannot describe our expanding universe. Here, we study instead the de Sitter thin brane model. This is described by the same action as that for the RS model, but the 4-dimensional space-time on the branes is $\rm dS_4$. We study the model for both the cases of positive 5-dimensional cosmological constant $\Lambda_5$ and negative one. In the positive $\Lambda_5$ case, the 4-dimensional large hierarchy necessitates a 5-dimensional large hierarchy, and we cannot get a natural explanation. On the other hand, in the negative $\Lambda_5$ case, the large hierarchy is naturally realized in the 5-dimensional theory in the same manner as in the RS model. Moreover, another large hierarchy between the Hubble parameter and the Planck scale is realized by the ${\mathcal O}(10^2)$ hierarchy of the 5-dimensional quantities. Finally, we find that the lightest mass of the massive Kaluza-Klein modes and the intervals of the mass spectrum are of order $10^2\,\rm GeV$, which are the same as in the RS case and do not depend on the value of the Hubble parameter.

Coulomb's law corrections and fermion field localization in a tachyonic de Sitter thick braneworld

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 solution of the gauge hierarchy problem, the localization of fermion fields in this model, the recovering of the Coulomb law on the non-relativistic limit of the Yukawa interaction between bulk fermions and gauge bosons localized in the brane, and confront the predicted 5D corrections to the photon mass with its upper experimental/observational bounds, finding the model physically viable since it passes these tests. In order to achieve the latter aims we first consider the Yukawa interaction term between the fermionic and the tachyonic scalar fields MF(T)ΨΨ̅ in the action and analyze four distinct tachyonic functions F(T) that lead to four different structures of the respective fermionic mass spectra with different physics. In particular, localization of the massless left-chiral fermion zero mode is possible for three of these cases. We further analyze the phenomenology of these Yukawa interactions among fermion fields and gauge bosons localized on the brane and obtain the crucial and necessary information to compute the corrections to Coulomb's law coming from massive KK vector modes in the non-relativistic limit. These corrections are exponentially suppressed due to the presence of the mass gap in the mass spectrum of the bulk gauge vector field. From our results we conclude that corrections to Coulomb's law in the thin brane limit have the same form (up to a numerical factor) as far as the left-chiral massless fermion field is localized on the brane. Finally we compute the corrections to the Coulomb's law for an arbitrarily thick brane scenario which can be interpreted as 5D corrections to the photon mass. By performing consistent estimations with brane phenomenology, we found that the predicted corrections to the photon mass, which are well bounded by the experimentally observed or astrophysically inferred photon mass, are far beyond its upper bound, positively testing the viability of our tachyonic braneworld. Moreover, the 5D parameters that define these corrections possess the same order, providing naturalness to our model, however, a fine-tuning between them is needed in order to fit the corresponding upper bound on the photon mass.

SLED phenomenology: curvature vs. volume

We assess the question whether the SLED (Supersymmetric Large Extra Dimensions) model admits phenomenologically viable solutions with 4D maximal symmetry. We take into account a finite brane width and a scale invariance (SI) breaking dilaton-brane coupling, both of which should be included in a realistic setup. Provided that the microscopic size of the brane is not tuned much smaller than the fundamental bulk Planck length, we find that either the 4D curvature or the size of the extra dimensions is unacceptably large. Since this result is independent of the dilaton-brane couplings, it provides the biggest challenge to the SLED program. In addition, to clarify its potential with respect to the cosmological constant problem, we infer the amount of tuning on model parameters required to obtain a sufficiently small 4D curvature. A first answer was recently given in [arXiv:1508.01124], showing that 4D flat solutions are only ensured in the SI case by imposing a tuning relation, even if a brane-localized flux is included. In this companion paper, we find that the tuning can in fact be avoided for certain SI breaking brane-dilaton couplings, but only at the price of worsening the phenomenological problem. Our results are obtained by solving the full coupled Einstein-dilaton system in a completely consistent way. The brane width is implemented using a well-known ring regularization. In passing, we note that for the couplings considered here the results of [arXiv:1508.01124] (which only treated infinitely thin branes) are all consistently recovered in the thin brane limit, and how this can be reconciled with the concerns about their correctness, recently brought up in [arXiv:1509.04201].

Gravity localization on hybrid branes

This work deals with gravity localization on codimension-1 brane worlds engendered by compacton-like kinks, the so-called hybrid branes. In such scenarios, the thin brane behaviour is manifested when the extra dimension is outside the compact domain, where the energy density is non-trivial, instead of asymptotically as in the usual thick brane models. The zero mode is trapped in the brane, as required. The massive modes, although are not localized in the brane, have important phenomenological implications such as corrections to the Newton's law. We study such corrections in the usual thick domain wall and in the hybrid brane scenarios. By means of suitable numerical methods, we attain the mass spectrum for the graviton and the corresponding wavefunctions. The spectra possess the usual linearly increasing behaviour from the Kaluza-Klein theories. Further, we show that the 4D gravitational force is slightly increased at short distances. The first eigenstate contributes highly for the correction to the Newton's law. The subsequent normalized solutions have diminishing contributions. Moreover, we find out that the phenomenology of the hybrid brane is not different from the usual thick domain wall. The use of numerical techniques for solving the equations of the massive modes is useful for matching possible phenomenological measurements in the gravitational law as a probe to warped extra dimensions.

Comment on “Localization of 5D Elko Spinors on Minkowski Branes”

We show that the statement in Liu et al. [Phys. Rev. D 86, 064012 (2012)] that the zero mode of Elko spinor is localized in some thin brane scenarios is not correct. This reopens the problem of localization of Elko spinors.

Classical tests of General Relativity in thick branes

Classical tests of General Relativity in braneworld scenarios have been investigated recently with the purpose of posing observational constraints on parameters of some models of infinitely thin brane. Here we consider the motion of test particles in a thick brane scenario that corresponds to a regularized version of the Garriga-Tanaka solution, which describes a black hole solution in RSII model, in the weak field regime. By adapting a mechanism previously formulated in order to describe the confinement of massive tests particles in a domain wall (that simulates classically the trapping of the Dirac field in a domain wall), we study the influence of the brane thickness on the four-dimensional (4D) path of massless particles. Although the geometry is not warped and, therefore, the bound motion in the transverse direction is not decoupled from the movement in the 4D-world, we can find an explicit solution for the light deflection and the time delay, if the motion in the fifth direction is a high frequency oscillation. We verify that, owing to the transverse motion, the light deflection and the time delay depend on the energy of the light rays. This feature may lead to the phenomenon of gravitational rainbow. We also consider the problem from a semi-classical perspective, investigating the effects of the brane thickness on the motion of the zero-mode in the 4D-world.

Warped brane worlds in critical gravity

We investigate the brane models in arbitrary dimensional critical gravity presented in Lu and Pope (Phys Rev Lett 106:181302, 2011). For the models of the thin branes with codimension one, the Gibbons–Hawking surface term and the junction conditions are derived, with which the analytical solutions for the flat, AdS, and dS branes are obtained at the critical point of the critical gravity. It is found that all these branes are embedded in an AdS $$_{n}$$ spacetime, but, in general, the effective cosmological constant $$\varLambda $$ of the AdS $$_{n}$$ spacetime is not equal to the naked one $$\varLambda _0$$ in the critical gravity, which can be positive, zero, and negative. Another interesting result is that the brane tension can also be positive, zero, or negative, depending on the symmetry of the thin brane and the values of the parameters of the theory, which is very different from the case in general relativity. It is shown that the mass hierarchy problem can be solved in the braneworld model in the higher-derivative critical gravity. We also study the thick brane model and find analytical and numerical solutions of the flat, AdS, and dS branes. It is found that some branes will have inner structure when some parameters of the theory are larger than their critical values, which may result in resonant KK modes for some bulk matter fields. The flat branes with positive energy density and AdS branes with negative energy density are embedded in an $$n$$ -dimensional AdS spacetime, while the dS branes with positive energy density are embedded in an $$n$$ -dimensional Minkowski one.

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.