G. Alencar

A transfer matrix method for resonances in Randall-Sundrum models

In this paper we discuss in detail a numerical method to study resonances in membranes generated by domain walls in Randall-Sundrum-like scenarios. It is based on similar works to understand the quantum mechanics of electrons subject to the potential barriers that exist in heterostructures in semiconductors. This method was used recently to study resonances of a three form field and lately generalized to arbitrary forms. We apply it to a lot of important models, namely those that contain the Gauge, Gravity and Spinor fields. In many cases we find a rich structure of resonances which depends on the parameters involved.

Antisymmetric tensor fields in Randall–Sundrum thick branes

Abstract In this Letter we study the issue of localization of the three-form field in a Randall–Sundrum-like scenario. We simulate our membrane by kinks embedded in D = 5 , describing the usual case (not deformed) and new models coming from a specific deformation procedure. The gravitational background regarded includes the dilaton contribution. We show that we can only localize the zero-mode of this field for a specific range of the dilaton coupling, even in the deformed case. A study about resonances is presented. We use a numerical approach for calculations of the transmission coefficients associated to the quantum mechanical problem. This gives a clear description of the physics involved in the model. We find in this way that the appearance of resonances is strongly dependent on the coupling constant. We study the cases p = 1 , 3 and 5 for α = − 1.75 and α = − 20 . The first value of α give us one resonance peak for p = 1 and no resonances for p = 3 , 5 . The second value of α give us a very rich structure of resonances, with number depending on the value of p.

A Transfer Matrix Method for Resonances in Randall-Sundrum Models II: The Deformed Case

A bstractHere we consider resonances of the Gauge, Gravity and Spinor fields in RandallSundrum-like scenarios. We consider membranes that are generated by a class of topological defects that are deformed domain walls obtained from other previously known ones. They are obtained by a deformation procedure generate different potentials to the associated Schrödinger-like equation. The resonance spectra are calculated numerically using the method of Transfer Matrix developed by the authors and presented in JHEP 1108 (2011) 071. The new deformed defects change the resonances spectra of all fields considered and the associated phenomenology as well.

On resonances of q-forms in thick p-branes

In this work we consider q form elds in a p brane embedded in a D = (p + 2) space-time. The membrane is generated by a domain wall in a RandallSundrum-like scenario. We study conditions for localization of zero modes of these elds. The expression agrees and generalizes the one found for the zero, one, two and three-forms in a 3 brane. By a generalization we mean that our expression is valid for any form in an arbitrary dimension with codimension one. We also point out that, even without the dilaton coupling, some form elds are localized in the membrane. The massive modes are considered and the resonances are calculated using a numerical method. We nd that dierent spaces have identical resonance structures, which we call dual spaces of resonances(DSR).

A transfer matrix method for resonances in Randall-Sundrum models III: an analytical comparison

A bstractThe transfer matrix method is used to analyze resonances in Randall-Sundrum models. Although it has successfully been used previously by us we provide here a comparison between the numerical and analytical models. To reach this we first find new exact solution for the scalar, gauge, Kalb-Ramond and q-form fields. Them we calculate numerically the resonances by the transfer matrix method and compare with the analytical result. For completeness, this is done for models with and without the dilaton coupling. The results show a perfect agreement between the analytical and numerical methods.

Solutions to the problem of ELKO spinor localization in brane models

Two different solutions to the problem of the zero-mode localization of the Elko spinor are presented. The first solution is given by the introduction of a mass term and by coupling the spinor with the brane through a delta function. The second solution is reached by a Yukawa geometrical coupling with the Ricci scalar. These two models consistently change the boundary condition at infinity and at the origin. For the case of the geometrical coupling, we are able to show that the zero mode is localized for any smooth version of the Randall-Sundrum model.

Gauge field localization on the brane through geometrical coupling

In this paper we consider a geometrical Yukawa coupling as a solution to the problem of gauge field localization. We show that upon dimensional reduction the vector field component of the field is localized but the scalar component (A5) is not. We show this for any smooth version of the Randall–Sundrum model. The covariant version of the model with geometrical coupling simplifies the generalization to smooth versions generated by topological defects. This kind of model has been considered some time ago, but there it has been introduced with two free parameters in order to get a localized solution which satisfy the boundary conditions: a mass term in five dimensions and a coupling with the brane. The boundary condition fixes one of them and the model is left with one free parameter M. First we show that by considering a Yukawa coupling with the Ricci scalar it is possible to unify these two parameters into just one fixed by the boundary condition. With this we get a consistent model with no free parameters and the mass term can be interpreted as a coupling to the cosmological constant.

Bulk Antisymmetric tensor fields coupled to a dilaton in a Randall-Sundrum model

A string-inspired three-form-dilaton-gravity model is studied in a Randall-Sundrum brane world scenario. As expected, the rank-3 antisymmetric field is exponentially suppressed. For each mass level, the mass spectrum is bigger than the one for the Kalb-Ramond field. The coupling between the dilaton and the massless Kaluza-Klein mode of the three-form is calculated, and the coupling constant of the cubic interactions is obtained numerically. This coupling are of the order of Tev{sup -1}; therefore, there exists a possibility to find some signal of it at Tev scale.

Antisymmetric tensor fields in codimension-two brane world

In this work we consider the issue of localization of antisymmetric tensor fields of arbitrary rank in a D-dimensional spacetime with a codimension-two membrane. A string-like defect is used to simulate the membrane. The localization of massless and massive fields is found. The mass spectrum is infinitely degenerate for each mass level and this is solved by coupling the q-form to fermions.

New analytical solutions for bosonic field trapping in thick branes

Abstract New analytical solutions for gravity, scalar and vector field localization in Randall–Sundrum (RS) models are found. A smooth version of the warp factor with an associated function f ( z ) = exp ( 3 A ( z ) / 2 ) inside the walls ( | z | d ) is defined, leading to an associated equation and physical constraints on the continuity and smoothness of the background resulting in a new space of analytical solutions. We solve this associated equation analytically for the parabolic and Poschl–Teller potentials and analyze the spectrum of resonances for these fields. By using the boundary conditions we are able to show that, for any of these solutions, the density probability for finding a massive mode in the membrane has a universal behavior for small values of mass given by | ψ m ( 0 ) | 2 = β 1 m + β 3 m 3 + β L m 3 log ( m ) + ⋯ . As a consequence, the form of the leading order correction, for example, to the Newtons law is general and does not depend on the potential used. At the end we also discuss why complications arise when we use the method to find analytical solutions to the fermion case.