RS brane-worlds do not rely on compactification to localize gravity at the brane, but on the curvature of the bulk (sometimes called “warped compactification”). What prevents gravity from ‘leaking’ into the extra dimension at low energies is a negative bulk cosmological constant,
where is the curvature radius of AdS_{5} and is the corresponding energy scale. The curvature radius determines the magnitude of the Riemann tensor: The bulk cosmological constant acts to “squeeze” the gravitational field closer to the brane. We can see this clearly in Gaussian normal coordinates based on the brane at , for which the AdS_{ 5} metric takes the form with being the Minkowski metric. The exponential warp factor reflects the confining role of the bulk cosmological constant. The Z_{2}-symmetry about the brane at is incorporated via the term. In the bulk, this metric is a solution of the 5D Einstein equations, i.e., in Equation (2). The brane is a flat Minkowski spacetime, , with self-gravity in the form of brane tension. One can also use Poincare coordinates, which bring the metric into manifestly conformally flat form, where .The two RS models are distinguished as follows:
We will concentrate mainly on RS 1-brane from now on, referring to RS 2-brane occasionally. The RS 1-brane models are in some sense the most simple and geometrically appealing form of a brane-world model, while at the same time providing a framework for the AdS/CFT correspondence [129, 342, 375, 193, 386, 390, 290, 347, 180]. The RS 2-brane introduce the added complication of radion stabilization, as well as possible complications arising from negative tension. However, they remain important and will occasionally be discussed.
http://www.livingreviews.org/lrr-2010-5 |
This work is licensed under a Creative Commons License. Problems/comments to |