The last waltz

In this book, we have presented a pedagogical review of some of the main developments in the study of brane worlds and extra dimensions. We have focussed on three main ideas: Large Extra Dimensions, Universal Extra Dimensions and Warped Extra Dimensions, and have dealt with these topics in considerable detail. We have also reviewed the theoretical ideas that are a necessary background to delve deep into these topics. However, from the time in the late 1990s when these new ideas of brane worlds and extra dimensions took shape, the subject has arborised in ways which would have been difficult to imagine then. We have concentrated on what in our view constitute the central ideas that would be of interest to students and researchers in high-energy physics but even as we focus on this flow, which we take to be the river we are acutely aware that there are several tributaries that we have not paid attention to. In fact, some of these tributaries have gained enough breadth and depth to be considered rivers in their own right. But we had to limit our task and focus on what we had set out to write about, else this river analogy would have been inadequate and we would have had to contend with an ocean. Nevertheless, it is possibly a good idea to leave the reader with an idea of some of these other topics that have not made it to the centre stage of our presentation. We do precisely this in this final chapter: a random walk, if you like, in the extra-dimensional world. In each case, we present a couple of references which deal with these subjects in much greater detail.

Neutrinos in extra dimensions

The last 15 years have seen the accumulation of a wealth of experimental data on neutrinos and there is now definite evidence for oscillations between the different neutrino generations showing that the three active neutrinos of the Standard Model are massive. More precisely, the experiments give information on the masssplittings, Δm2 between the neutrinos, and these are typically of the order of 10−3 eV2. Typically, one would bring in a right-handed fermion NR which is, as discussed in Chapter 2, a Standard Model singlet.