Randall-Sundrum Research Articles

Constraining integrable AdS/CFT with factorized scattering

We consider (warped) AdS string backgrounds which allow for a GKP spinning string/null cusp solution. Integrability implies that the worldsheet S-matrix should factorize, which in turn constrains the form of the warp factor as a function of the coordinates of the internal space. This constraint is argued to rule out integrability for all supersymmetric AdS7 and AdS6 backgrounds as well as AdS5 Gaiotto-Maldacena backgrounds and a few highly supersymmetric AdS4 and AdS3 backgrounds.

Braneworld mimetic f(R) gravity

Following our recent work on braneworld mimetic gravity, in this paper, we study an extension of braneworld mimetic gravity to the case that the gravitational sector on the brane is modified in the spirit of [Formula: see text] theories. We assume the physical 5D bulk metric in the Randall–Sundrum II braneworld scenario consists of a 5D scalar field (which mimics the dark sectors on the brane) and an auxiliary 5D metric. We find the 5D Einstein’s field equations and the 5D equation of motion of the bulk scalar field in this setup. By using the Gauss–Codazzi equations, we obtain the induced Einstein’s field equations on the brane. Finally, by adopting the FRW background, we find the Friedmann equation on the brane in this [Formula: see text] mimetic braneworld setup.

Conformal invariant gravity coupled to a gauged scalar field and warped spacetimes

Abstract We investigate the conformal invariant Lagrangian of the self-gravitating U(1) scalar-gauge field on the time-dependent Bondi–Marder axially symmetric spacetime. By considering the conformal symmetry as exact at the level of the Lagrangian and broken in the vacuum, a consistent model is found with an exact solution of the vacuum Bondi–Marder spacetime, written as g μ ν = ω 2 g μ ν , where ω is the conformal factor and g μ ν the ‘un-physical‘ spacetime. Curvature could then be generated from Ricci-flat g μ ν by suitable dilaton fields and additional gauge freedom. If we try to match this vacuum solution on the interior vortex solution of the coupled Einstein-scalar-gauge field, we need, besides the matching conditions, constraint equations in order to obtain a topological regular description of the small-scale behaviour of the model. Probably, one needs the five-dimensional warped counterpart model, where the warp factor determines the large-scale behaviour of the model. The warped five-dimensional model can be reformulated by considering the warp factor as a dilaton field conformally coupled to gravity and embedded in a smooth M 4 ⊗ R manifold. Dark energy and the cosmological constant could then be emergent in this model. The dilaton field has a dual meaning. At very early times, when ω → 0 , it describes the small-distance limit, while at later times it manifests itself as a warp (or scale) factor that determines the dynamical evolution of the universe. However, as expected, the conformal invariance is broken (trace-anomaly) by the appearance of a mass term and a quadratic term in the energy–momentum tensor of the scalar-gauge field, arising from the extrinsic curvature terms of the projected Einstein tensor. By considering the dilaton field and Higgs field on equal footing on small scales, there will be no singular behaviour, when ω → 0 and one can deduce constraints to maintain regularity of the action.

Are there braneworld models that have complete localization properties?

A braneworld model is a model of (1+3+N)-dimensional space-time, called the bulk, with N extra dimensions where standard model particles are assumed to be localized on a (1+3)-dimensional “surface”, the so-called brane, embedded in the bulk. Gravitational fields, on the other hand, may propagate in the full space, the bulk. Some of the models could explain the weakness of the gravitational force relative to the other fundamental forces of nature. Among various models, the Randall-Sundrum (RS) model, an N = 1 braneworld model, has attracted much attention. Unfortunately, the assumption that standard model particles are trapped on the RS brane is not fully fulfilled. Accordingly, one of us with other colleagues proposed a modified RS model. The new model is conformally flat space-time and has much better localization properties. However, it is still not a perfect braneworld model since matter fields in some configurations are not localizable. This paper will elaborate localization properties of the model and discussed possible further modification to have a perfect model in terms of localization properties.

Universal aspects of U(1) gauge field localization on branes in D-dimensions

In this work, we study the general properties of the D-vector field localization on (D − d − 1)-brane with co-dimension d. We consider a conformally flat metric with the warp factor depending only on the transverse extra dimensions. We employ the geometrical coupling mechanism and find an analytical solution for the U(1) gauge field valid for any warp factor. Using this solution we find that the only condition necessary for localization is that the bulk geometry is asymptotically AdS. Therefore, our solution has an universal validity for any warp factor and is independent of the particular model considered. We also show that the model has no tachyonic modes. Finally, we study the scalar components of the D-vector field. As a general result, we show that if we consider the coupling with the tensor and the Ricci scalar in higher co-dimensions, there is an indication that both sectors will be localized. As a concrete example, the above techniques are applied for the intersecting brane model. We obtain that the branes introduce boundary conditions that fix all parameters of the model in such a way that both sectors, gauge and scalar fields, are confined.

Graviton KK resonant modes in the correction of Newton's law from six-dimensional braneworlds

In this work, we derive an expression for the corrections in Newton's law of gravitation due to gravitational Kaluza-Klein (KK) states in a general thick string-like braneworld scenario in six dimensions (6D). The correction has an exponentially suppressed mass term and depends on the values of the eigenfunctions and warp factors computed at the peak of the brane. Besides, we use suitable numerical methods to analyze such corrections in a 3-brane placed in a transverse Resolved Conifold (RC), wherein we attain the massive KK spectrum and its corresponding eigenfunctions. The spectrum is real and monotonically increasing. The RC model has a parameter, known as the resolution parameter, which removes the conical singularity and we conclude that such parameter must assume moderate values to have physically acceptable states. Moreover, the trapped massless mode regains the 4D gravity, and it is displaced from the origin, sharing a similar profile with the energy density of brane for small values of the resolution parameter. Finally, we found for the singular RC a resonant mode which is the seventh eigenfunction in the KK mass tower. Such an excited state is the most accountable massive mode in the computation of the deviations in the Newtonian potential. Moreover, the bounds to RC parameters are briefly discussed as a perspective to fit the current experimental data.

Higgs vacuum decay from particle collisions?

We examine the effect of large extra dimensions on black hole seeded vacuum decay using the Randall-Sundrum model as a prototype for warped extra dimensions. We model the braneworld black hole by a tidal solution, and solve the Higgs equations of motion for the instanton on the brane. Remarkably, the action of the static instanton can be shown to be the difference in the bulk areas of the seed and remnant black holes, and we estimate these areas assuming the black holes are small compared to the bulk AdS radius. Comparing to the Hawking evaporation rate shows that small black hole seeds preferentially catalyse vacuum decay, thus extending our previous results to higher dimensional braneworld scenarios. The parameter ranges do not allow for Standard Model Higgs decay from collider black holes, but they can be relevant for cosmic ray collisions.

Quark-Antiquark Potential from a Deformed AdS/QCD

In this work we calculate the static limit of the energy for a quark-antiquark pair from the Nambu-Goto action using a holographic approach with a deformed AdS space, with warp factor exp⁡{(κz)n/n}. From this energy we derive the Cornell potential for the quark-antiquark interaction. We also find a range of values for our parameters which fits exactly the Cornell potential parameters. In particular, setting the zero energy of the Cornell potential at 0.33 fermi, we find that κ=0.56 GeV and n=1.3.

Inflationary RSII model with a matter in the bulk and exponential potential of tachyon field

In this paper, we study a tachyon cosmological model based on the dynamics of a 3-brane in the second Randall-Sundrum (RSII) model extended to include matter in the bulk. The presence of matter in the bulk changes the warp factor which leads to the modification of inflationary dynamics. The additional brane behaves effectively as a tachyon. We calculate numerically observation parameters of inflation: the scalar spectral index (ns) and the tensor-to-scalar ratio (r) for the exponential potential of the tachyon field.

Nonlinear interactions of the radion field

We study the Randall-Sundrum model with two branes. The Standard Model fields are localized on the brane with a negative tension, the gravitational field and scalar Goldberg-Wise field propagate in the multidimensional bulk. For this model we construct the Lagrangian for the scalar fluctuations of the gravitational and scalar fields above a background solution. We obtain an effective four-dimensional Lagrangian, which contains nonlinear self-interaction terms of the radion field up to the fourth order and nonlinear interactions of the radion and the Standard Model fields.

Warm DBI inflation with constant sound speed

We study inflation with the Dirac–Born–Infeld (DBI) noncanonical scalar field in both the cold and warm scenarios. We consider the Anti-de Sitter warp factor f(phi )=f_{0}/phi ^{4} for the DBI inflation and check viability of the quartic potential V(phi )=lambda phi ^{4}/4 in light of the Planck 2015 observational results. In the cold DBI setting, we find that the prediction of this potential in the r-n_s plane is in conflict with Planck 2015 TT, TE, EE + low P data. This motivates us to focus on the warm DBI inflation with constant sound speed. We conclude that in contrary to the case of cold scenario, the r-n_s result of warm DBI model can be compatible with the 68% CL constraints of Planck 2015 TT, TE, EE + low P data in the intermediate and high dissipation regimes, whereas it fails to be observationally viable in the weak dissipation regime. Also, the prediction of this model for the running of the scalar spectral index dn_s/dln k is in good agreement with the constraint of Planck 2015 TT, TE, EE + low P data. Finally, we show that the warm DBI inflation can provide a reasonable solution to the swampland conjecture that challenges the de Sitter limit in the standard inflation.

U(1) gauge vector field on a codimension-2 brane

In this paper, we obtain a gauge invariant effective action for a bulk massless U(1) gauge vector field on a brane with codimension two by using a general Kaluza-Klein (KK) decomposition for the field. It suggests that there exist two types of scalar KK modes to keep the gauge invariance of the action for the massive vector KK modes. Both the vector and scalar KK modes can be massive. The masses of the vector KK modes m(n) contain two parts, m1( n) and m2( n), due to the existence of the two extra dimensions. The masses of the two types of scalar KK modes mϕ( n) and mφ( n) are related to the vector ones, i.e., mϕ( n) = m1( n) and mφ( n) = m2( n). Moreover, we derive two Schrödinger-like equations for the vector KK modes, for which the effective potentials are just the functions of the warp factor.

Fermion localization on branes with non-standard kinetic terms

In this paper, by using the Yukawa coupling mechanism, we consider the fermion localization in two types of braneworld models driven by real scalar fields with non-standard dynamics. Because of the existing freedom in the form of the Yukawa coupling, we consider two coupling forms between the background scalar field and spinors where one is arising from the geometry shape of the warp factor and the other is a function of the background scalar field containing a derivative scalar-fermion coupling. With two coupling functions, it is shown that the massless zero mode of fermion fields is localized on both branes with generalized dynamic depending on the values of the coupling constants. However, there is no localized mode when the Yukawa coupling only contains a derivative term of the background scalar field. Furthermore, effects of the parameters of the models on the zero mode and fermion effective potential are addressed.

The The Bhabha Scattering in the Randall-sundrum Model

The change in other two fermion processes is called Bhabha process. In this paper, we discuss the Bhabha process in the Randall –Sundrum (RS). We caculated the cross section for photon , boson Z, radion and Higgs h exchange and evaluated exchange contributions of the Bhabha process in detail. 
 Keywords: DCS, cross-section, Bhabha, radion, Randall-Sundrum.
 References
 [1] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370, 1999.[2] H. Davoudiasl, T. McElmurry and A. Soni, Phys. Rev. D82, 115028, 2010.[3] V. P. Goncalves and W. K. Sauter, Phys. Rev. D82, 056009, 2010. [4] W. -J. Zhang, W. -G. Ma, R. -Y. Zhang, X. -Z. Li, L. Guo, and C. Chen, Phys. Rev. D92, 116005, 2015, [arXiv:1512.01766].[5] C. Cai, Z.-H. Yu and H.-H. Zhang, Phys. Rev. D93. 075033, 2016.[6] F. Abu-Ajamieh, R. Houtz, and R. Zheng, [arXiv: 1607.01464v1 [hep-ph]], 2016.[7] The CMS Collaboration, CERN, August 2016.[8] The CMS Collaboration, CERN, September 2016.[9] F. Richard, [ arXiv:1804.02846 [hep-ex]], 2018.

Tachyon scalar field in a braneworld cosmology

We analyze a tachyon cosmological model based on the dynamics of a 3-brane in the bulk of the second Randall–Sundrum model. This model contains extended general warp functions, i.e. generalized bulk geometry. We study a power law warp factor in cosmological context. This type of warp factor generates an inverse power law tachyonic potential.

Generalization of the Randall-Sundrum Model Using Gravitational Model F(T,Θ)

In this letter, we explore a generalized model based on two scenarios including the Randall-Sundrum model and gravity model F(T,Θ). We first study the standard Randall-Sundrum gravitational model and then add a function containing two parameters as torsion and trace energy-momentum tensor to the main action of the model. Next, we derive the equations of the generalized model and obtain a new critical value for the energy density of the brane. The results showed that inflation and the dark energy-dominated stage can be realized in this model. We pointed out one significant category of dark energy models that had greatly developed the knowledge about dark energy. To be specific, dark energy could either be quintessence-like, phantom-like, or the so-called “quintom”-like. The models of quintom type suggest that the equation of state parameter of dark energy can cross the cosmological constant boundary ω=-1. Interestingly, this quintom scenario exactly appeared in this paper.

Subregion complexity and confinement–deconfinement transition in a holographic QCD model

We study the subregion complexity in a semi-analytical holographic QCD model. Two cases with different warped factor are considered and both can realize confinement–deconfinement transition. By studying the behavior of the renormalized holographic complexity density Cˆ versus the subregion length scale ℓ, we find that for both cases, Cˆ always experiences a discontinuity at certain critical value ℓc in confinement phases, while it is always continuous in deconfinement phases. This property may be seen as a signal to characterize confinement or deconfinement phases. The behavior of Cˆ versus the temperature and chemical potential is also investigated and our results show that Cˆ exhibits behavior characterizing the type of the transition. That is, it experiences a discontinuity at the transition temperature for μ<μc where first-order confinement–deconfinement phase transition happens, while it is always continuous for μ>μc where the transition turns into a turnover. These results imply that the renormalized holographic complexity density may be used as a good parameter to characterize the corresponding phase structures.

Localization of matter fields that interact with gravity in a non-minimal derivative coupling in the Randall-Sundrummodel

In a brane-world model matter fields are assumed to localize on a (3 + 1)-dimensional brane imbedded in a higher dimensional space-time. However, this assumption is not always fulfilled. In fact, vector fields that couple minimally with gravity as well as matter fields that interact with gauge fields, in addition to gravity in a minimal coupling way are not localized on a brane in the five-dimensional Randall-Sundrum (RS) model [1, 2, 3]. In this paper we will report our analysis on localization properties in the RS brane-world model for the case of matter fields that interact with gravity in a non-minimal derivative coupling. By expressing matter fields as a multiplication of fields in a four-dimensional space-time and a function of the extra dimension coordinate we derive localization conditions and field equations in the function of the extra coordinate and solve the equation. The solution is then applied to analyze field localizations. We obtain that the massless scalar and spinor fields are localizable respectively on the RS brane for decreasing and increasing warp factor respectively.

Hierarchy problem and new warped extra dimension

In this paper, we propose a new mechanism with warped extra dimension to solve the hierarchy problem, which is parallel to the Randall-Sundrum (RS) brane scenario. Different from the RS scenario, the fundamental scale is TeV scale and the four-dimensional Planck scale is generated from the exponential warped extra dimension at size of a few TeV$^{-1}$. The experimental consequences of this scenario are very different from that of the RS scenario. In the explicit realization in the nonlocal gravity theory, there is a tower of spin-2 excitations with mass gap $10^{-4}\text{eV}$ and they are coupled with the gravitational scale to the standard model particles. We further discuss the possible generalizations in other modified gravity theories. The experimental consequences are similar to $(4+N)$-dimensional large extra dimension but $N$ can be a non-integer, which satisfies the experimental constraints more easily than the integer large extra dimension model.

Thermodynamic Prescription of Cosmological Constant in the Randall-Sundrum II Brane

In this work, we apply the quantum corrected entropy function derived from the Generalized Uncertainty Principle (GUP) to the holographic equipartition law to study the cosmological scenario in the Randall-Sundrum (RS) II brane. An extra driving term has come up in the effective Friedmann equation for a homogeneous, isotropic, and spatially flat universe. Further, thermodynamic prescription of the universe constraints this term eventually with an order equivalent to that of the cosmological constant.