Lisa Randall and Raman Sundrum proposed the 5-dimensional warped geometry theory (also referred to as the Randall-Sundrum model) in 1999.  They were looking to solve the hierarchy problem of the Standard Model; that is, why the other three forces are so much stronger than gravity.  Their solution, in simplistic terms, is a five dimensional (four of space, one of time) Universe containing four dimensional (three of space, one of time) brane(s).  The two branes are the "gravity brane", where gravitons exist, and the "weak brane" for all the other elementary particles.  The weak brane is "our" world.  The two branes are separated in the fifth dimension and carry opposite brane energy, which has the affect of warping the fifth dimension.  Gravity is strong on the gravity brane, but falls off as it crosses over to the weak brane.  The separation proposed is such that the strength of gravity is equal to what we measure when it reaches the weak brane.  This implies a change of 16 orders of magnitude.  By applying this to superstring theory, the strings are the proposed length of 10-33 cm on the gravity brane, but enlarge by 16 orders of magnitude to 10-17 cm on the weak brane.  In this model, therefore, it is possible that strings could be detected by the LHC in the future.  A second version of the model proposes that, rather than being a fixed length, the fifth dimension is, essentially, infinite putting the two branes infinitely far apart, with gravity having its "natural home" in the bulk.

In the
Randall-Sundrum Model, all the fundamental particles and forces (except gravity and gravitons) are represented as open strings that have their ends stuck in our 3-brane, the Weak brane, and cannot extend into the extra, warped dimension or into any of the other possible branes within that bulk.  Photons, for example, cannot leave our brane or enter it from the bulk, so that all we see is the three space plus one time dimension of our Universe.  Gravity and gravitons are represented as closed loop strings that exist either in the bulk, or in another brane, the Gravity brane.

It is very difficult to discuss this model without mathematics, although Lisa Randall does an excellent job in her book "Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions", which I
recommend enthusiastically .  Thoughtcast has an excellent interview with Lisa Randall on the Randall-Sundrum Model, and Scientific American has an article on Branes about the work of Lisa Randall.  The Cornell University Library has a somewhat mathematical analysis of many multi-dimensional theories; refer to the section on Warped Extra Dimensions.  Finally an article by Lisa Randall published in Science.

Physics