The motivation

In the previous chapter, we presented a detailed exposition of the original version of the Randall-Sundrum model, also known as the RS1 model. In this next chapter, we will discuss variations and extensions of the original model. The primary difference is that the gauge fields and the fermions of the Standard Model are no longer confined to the TeV brane and so we first need to discuss how to deal with these fields when they propagate in the extra dimension. This is what we will take up first.

Let us first try to understand the motivation to go beyond the minimal Randall–Sundrum or RS1 model. In the RS1 model, the exponential warp factor involving the fifth-dimensional co-ordinate results in a conformal rescaling of the fields localised on the TeV brane and it thus provides a solution to the gaugehierarchy problem. As explained in the previous chapter, this solution is complete once the stablisation of the model, using the Goldberger-Wise mechanism, is achieved.

Trying to address the hierarchy problem in this fashion, however, forces us to reckon with attendant issues. One issue is that since any mass scale associated with the fields localised on the TeV brane is rescaled towards the infrared by e−kL, it also affects mass scales which need to be large and not get warped down to TeV scales. Such mass scales, for example, are those which suppress higherdimensional operators associated with proton decay, flavour-changing neutral currents (FCNCs) or neutrino masses. In the usual four-dimensional theories, these operators are suppressed by a large mass scale M which is typically in the range of 1012 − 1015 GeV related to the scale of grand unification or left–right symmetry-breaking. But in the RS1 model these get redshifted to roughly a TeV, which then has obvious disastrous consequences.

One way out of this problem could be using discrete symmetries to forbid these operators but this is an unwieldy procedure. A much simpler solution is bulk. The point is that to address the hierarchy problem only the Higgs field needs to be localised on the TeV brane – it is not necessary to have the fermions and gauge bosons so localised.