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

Abstract

We construct the nonlocal braneworld action in the two-brane Randall-Sundrum model in a holographic setup alternative to Kaluza-Klein description: the action is written as a functional of the two metric and radion fields on the branes. This action effectively describes the dynamics of the gravitational field both on the branes and in the bulk in terms of the brane geometries directly accessible for observations. Its nonlocal form factors incorporate the cumulative effect of the bulk Kaluza-Klein modes. We also consider the reduced version of this action obtained by integrating out the fields on the negative-tension brane invisible from the viewpoint of the Planckian brane observer. This effective action features a nontrivial transition (AdS flow) between the local and nonlocal phases of the theory associated with the limits of small and large interbrane separation. Our results confirm a recently proposed braneworld scenario with diverging (repulsive) branes and suggest possible new implications of this phase transition in brane cosmology.

Duality of boundary value problems and braneworld action in curved brane models

“…For flat 4-dimensional branes, R(g) = 0, d = 4, this expression reduces to the result obtained in [14] 11 .…”

“…These properties of the braneworld formalism were considered in much detail in a number of papers [14,21,22] where the location of branes in the bulk was described in the Gaussian normal coordinates, G yy = 1, G yµ = 0, by an additional scalar field -the radion.…”

“…We will calculate the braneworld effective action defined by the procedure that was discussed in much detail in [14]. In contrast to the conventional Kaluza-Klein reduction, usually used for the construction of the effective action [18,19], our action is a functional of the fields that have direct physical and geometrical interpretation.…”

“…In contrast to the results of these works we concentrate on two-brane models with independent metric configurations on their branes. This is done along the lines of the previous papers [13,14] where the weak field (quadratic in perturbations) approximation for braneworld action was obtained on the background of flat branes. In distinction from [7,9,10] we obtain the nonlocal action nontrivially intertwining metric fields on both branes.…”

“…Its derivation is based on the technique of linearized invariants of the diffeomorphism gauge transformations intensively used in the theory of cosmological perturbations [15,16,17]. Sect.4 gives a review of the alternative calculation [14] of the same result, based on its recovery from the effective equations of motion. In Sect.5 we show the equality of the two manifestly different quadratic forms of the action by proving that their kernels are equal to one another -the main duality relation between specific operators of the Dirichlet and Neumann boundary value problems.…”