On the stabilization of the size of extra dimensions

Abstract

We derive a general formalism for constructing a four-dimensional effective action for the radion field in 5 dimensions, taking into account the possible dependence of the scale factor on the internal coordinate. First and second variations of the action with respect to the size of the extra dimension reveals two types of algebraic constraints on the combination of brane and bulk Lagrangians that extremize the action, and provide an effective mass for the radion field. We derive a compact formula for the radion mass squared in terms of brane and bulk potentials for the case of a bulk scalar field. We further specialize these constraints for several, five-dimensional realizations of brane world models.

Ghosts and Tachyons in the Fifth Dimension

“…This situation is different from the sinh-type solution where both stable and unstable configurations are possible [17].…”

“…In this paper we generalize the results of [16,17] that find the solutions to the scale factor and analyze the radion stability in the 5D models with conventional bulk scalar. We consider models that admit scalar fields that has the "wrong" sign of the kinetic term.…”

“…Following the method of Ref. [17], we calculate the second variation of the effective action over the scale factor b and use boundary conditions to simplify the answer. The result can be presented as a sum of two terms evaluated at the position of the branes,…”

On the stabilization of modulus in Randall–Sundrum model by RΦ2 interaction

“…In order to investigate the case of finite quartic coupling, we must calculate the first and second derivatives of the effective potential. By using eqs (11), (12) and after a lengthy calculation we get…”

“…Their solution involved a massive bulk scalar field with the usual kinetic term in the bulk and quartic interactions localized on the two branes. Since then, many studies have appeared on this subject [3][4][5][6][7][8][9][10][11][12]. The studies of refs [3,4] consider models for the stabilization of the modulus containing a bulk scalar field interacting with the space-time curvature R.…”