The Brane-World

As we have seen, the present understanding of string theory indicates that all the different 10-dimensional string theories (types I, IIA, IIB and two heterotic) happen to be different manifestations of a single $M$- theory. It has also led to a prime role played by high dimensional surfaces known as D-branes, giving support to the idea that our 4-dimensional world could itself be a brane. The brane world scenario has been subject to intense investigation during the past two years and new interesting mechanisms have been proposed to solve longstanding problems with the standard model, such as the hierarchy problem, gauge coupling unification, neutrino masses, strong CP problem, etc. Here we will only overview the subject, for a more complete review see for instance the article by E. Dudas in [7] and a forthcoming article by Arkani-Hamed et al. One of the interesting properties of this scenario is that it allows for a fundamental scale of nature to be much below the Planck scale and therefore closer to experiments. However until recently explicit realizations of this scenario, with low-energy fundamental scale, were lacking. We review here the progress we have made in that direction during the past few months.

This is a variation of a Kaluza-Klein theory for which the extra dimensions are felt only by a subset of the fields. The typical case is that the Standard Model fields are constrained to live inside a low dimensional surface, or brane, of the high dimensional spacetime, but gravity lives in the full spacetime [54]. This seems like a ad-hoc separation of the fields, however recent developments on string theory precisely point at this scenario. The Horava-Witten realization of strongly coupled heterotic string, leads after compactification, to a 5D world with the 5th coordinate being just an interval. Gauge and matter fields live only on the two 4D surfaces at each end of the interval, whereas gravity lives in the full 5D spacetime. Similarly, and more relevant for this talk, type I string theory includes Dp-branes. These are surfaces where the end points of the open strings are attached, satisfying Dirichlet boundary conditions, here the origin of the name D-branes. The surfaces may be of different dimensionality which is denoted by $p$. Each Dp-brane has a $U(1)$ gauge field corresponding to an open string with both endpoints on the same brane. There are also states corresponding to open strings with endpoints on two different branes, the mass of these states is proportional to the distance between the branes, therefore when two branes overlap, the distance vanishes and these states become massless with the net effect of enhancing the gauge symmetry from $U(1)^2$ to $U(2)$. If there are $N$ overlapping branes the gauge symmetry will then be $U(N)$. On the other hand, gravity corresponds to closed strings and these can move on the whole 10-dimensional spacetime. Therefore we have a clean realisation of the brane world scenario in type I string theory with $U(N)$ (or other groups) living on the brane and gravity on the bulk.

Figure 4: A cartoon version of a typical brane world. Our Universe fits into an surface (the observable brane) inside a higher dimension space (the bulk). There are other branes which are hidden to us because they only couple to the bulk through gravity. The open strings representing the matter fields have their endpoints attached to the brane (a D-brane) whereas gravity only comes from the closed strings which are free to move in the bulk.