Effective Lagrangians for physical degrees of freedom in the Randall$ndash$Sundrum model

Abstract

We derive the second variation Lagrangian of the Randall -Sundrum model with two branes, study its gauge invariance and diagonalize it in the unitary gauge. We also show that the effective fourdimensional theory looks different on different branes and calculate the observable mass spectra and the couplings of the physical degrees of freedom of 5-dimensional gravity to matter.

Gravi-Reggeons and trans-Planckian scattering in models with one extra dimension

“…The coordinates x µ are Galilean on the visible brane. It is not surprising that the relations (8) and (9) are reproduced in this scheme.…”

“…One can, however, introduces the Galilean coordinates z µ = x µ e −πκr and rewrite both the gravitational field and the energy-momentum tensor in these coordinates (see, for instance, reviews [8]). Then the warp factor is equal to 1 at the negative tension brane, and a correct determination of the masses on this brane can be achieved [9]. By calculating the zero mode sector of the effective theory one thus obtains:…”

“…(2) and (4) (assuming that κ ∼M 5 ∼M P l ). We will derive analogous bounds on the ratio κ/M 5 , when the SM fields are on the negative tension brane with the Galilean coordinates, and, consequently, relations (8), (9) are valid (assuming that κ M 5 ∼ 1 TeV). We exploit the ideas used in the above mentioned paper [7].…”

Nonlocal braneworld action: An alternative to the Kaluza-Klein description

“…Indeed, given the action (11) as a result of solving the Dirichlet problem (8), (10), one can further apply the variational procedure, now with respect to the induced metric g µν , to get the effective equations…”

“…This observation suggests two equivalent methods of recovering the braneworld effective action. One method is straightforward -the direct substitution of the solution G AB = G AB [ g µν (x) ] of the Dirichlet problem (8), (10) into the five-dimensional action. The other method, which we choose to pursue in the following, is less direct, but technically is simpler.…”