It was also discovered that p-branes, which are
extended objects of higher dimension than strings (1-branes), play
a fundamental role in the theory. In the weak coupling limit,
p-branes () become infinitely heavy, so that they
do not appear in the perturbative theory. Of particular importance
among p-branes are the D-branes, on which open strings can end.
Roughly speaking, open strings, which describe the
non-gravitational sector, are attached at their endpoints to
branes, while the closed strings of the gravitational sector can
move freely in the bulk. Classically, this is realised via the
localization of matter and radiation fields on the brane, with
gravity propagating in the bulk (see Figure 1
).
|
|
In the ADD models, more than one extra dimension
is required for agreement with experiments, and there is
“democracy” amongst the equivalent extra dimensions, which are
typically flat. By contrast, the RS models have a “preferred” extra
dimension, with other extra dimensions treated as ignorable (i.e.,
stabilized except at energies near the fundamental scale).
Furthermore, this extra dimension is curved or “warped” rather than
flat: The bulk is a portion of anti-de Sitter () spacetime. As in the Horava-Witten solutions, the
RS branes are
-symmetric (mirror symmetry), and have a
tension, which serves to counter the influence of the negative bulk
cosmological constant on the brane. This also means that the
self-gravity of the branes is incorporated in the RS models. The
novel feature of the RS models compared to previous
higher-dimensional models is that the observable 3 dimensions are
protected from the large extra dimension (at low energies) by
curvature rather than straightforward compactification.
The RS brane-worlds and their generalizations (to
include matter on the brane, scalar fields in the bulk, etc.)
provide phenomenological models that reflect at least some of the
features of M theory, and that bring exciting new geometric
and particle physics ideas into play. The RS2 models also provide a
framework for exploring holographic ideas that have emerged in
M theory. Roughly speaking, holography suggests that
higher-dimensional gravitational dynamics may be determined from
knowledge of the fields on a lower-dimensional boundary. The
AdS/CFT correspondence is an example, in which the classical
dynamics of the higher-dimensional gravitational field are
equivalent to the quantum dynamics of a conformal field theory
(CFT) on the boundary. The RS2 model with its metric satisfies this correspondence to lowest
perturbative order [87
] (see
also [254
, 282
, 136
, 289
, 293
, 210
, 259
, 125
] for the AdS/CFT
correspondence in a cosmological context).
In this review, I focus on RS brane-worlds
(mainly RS 1-brane) and their generalizations, with the emphasis on
geometry and gravitational dynamics (see [219, 228, 190, 316, 260, 185, 267, 79, 36, 189, 186
] for previous
reviews with a broadly similar approach). Other recent reviews
focus on string-theory aspects, e.g., [101, 231, 68, 264], or on particle
physics aspects, e.g., [262, 273, 182, 112, 51
]. Before turning to
a more detailed analysis of RS brane-worlds, I discuss the notion
of Kaluza-Klein (KK) modes of the graviton.