Introduction

We have seen in the previous chapters that the ADD model of large extra dimensions provides us with a rich phenomenology which is currently being explored in high-energy experiments. However, soon after the ADD model was first studied, it was realised that, in the absence of a mechanism that will stabilise the large radii of compactification, the large disparity between the radii of compactification and the four-dimensional Planck radius shows up as a residual hierarchy. This was historically the main motivation to look for models without large extra dimensions and it was this search that led to the development of the warped extra-dimensional model of Randall and Sundrum [26]. In the meantime, however, a study of Calabi-Yau flux compactifications in Type II B string theory with all moduli stabilised has shown how stable, large-volume compactifications naturally arise in this context. While it seems difficult to generate millimetresized extra dimensions in this scenario, it is easily possible to generate a whole range of large compactification radii and also have physics related to a variety of scales from the Planck scale to the TeV scale [192, 193, 194].

This demonstration of how large extra dimensions can arise in generic string models has taken the sting out of the original motivation for warped extra dimensional models. But there are other reasons, equally compelling, to study warped extra dimensional models. For one, it provides a completely novel way of addressing the hierarchy problem. Moreover, it allows one to think of curvature in the extra dimensions. The ADD model assumes flat extra dimensions. The assumption that is being made is that the presence of the branes does not significantly distort the flat extra-dimensional metric. This is not a good assumption if brane tensions are not negligible. In fact, the possibility of curved extra dimensions brings in a bonus: the cosmological constant in the bulk can be adjusted so as to get an effective vanishing 4-d cosmological constant. The bulk cosmological constant allows one to compensate for the effect of the back-reaction of gravity to the branes and, in effect, from the view-point of an observer on the brane the four-dimensional universe will appear static and flat.