Massive p-form trapping as a p-form on a brane

I C Jardim,R R Landim,G Alencar,R N Costa Filho

doi:10.1007/jhep04(2015)003

Abstract

It is shown here that the zero mode of any form field can be trapped to the brane using the model proposed by Ghoroku and Nakamura. We start proven that the equations of motion can be obtained without splitting the field in even and odd parts. The massive and tachyonic cases are studied revealing that this mechanism only traps the zero mode. The result is then generalized to thick branes. In this scenario, the use of a delta like interaction of the quadratic term is necessary leading to a "mixed" potential with singular and smooth contributions. It is also shown that all forms produces an effective theory in the brane without gauge fixing. The existence of resonances with the transfer matrix method is then discussed. With this we analyze the resonances and look for peaks indicating the existence of unstable modes. Curiously no resonances are found in opposition of other models in the literature. Finally we find analytical solutions for arbitrary $p-$forms when a specific kind of smooth scenario is considered.

Highlights

JHEP04(2015)003 to compactification [8]
In this paper we further developed the model proposed by Ghoroku and Nakamura in [18] and apply it to p-form fields
We calculate the value of the coupling parameter with the brane, c, which localizes the zero mode of the transversal part of the vector field

Summary

Five dimensional Proca model in a thin brane scenario

As mentioned in the introduction, the action used in this paper is the following. this is the Proca action with a coupling term with the brane used in [18]. Where the prime means a derivative in z The former is the equation of a reduced massive gauge field, while the later is the equation governing the localization factor f (z). For tachyonic modes, taking mX → imX in (2.25), we obtain a non-localized solution given by modified Bessel functions with a condition of coefficients similar to (2.26). As we have fixed c to localize the zero mode of vector field is not possible vanish the divergent part of scalar field solution. The potential for scalar field is the same of vector field, changing only the boundary condition, the behavior of massive and tachyonic modes are the same, i.e, non-localized. In the same way that we can not vanish f1 due the boundary condition is not possible vanish the divergent part of longitudinal vector field.

The Kalb-Ramond case

The p-form case

The p-form case in a smooth warp factor scenario

Conclusion