In this post, the mathematics applies to both, Randall-Sundrum-1and-2 models, hence I will not distinguish between them here. One of the most powerful aspects of M-theory’s braneworld scenarios is that the bosonic and fermionic fields of the Standard Model of physics can be interpreted as low-lying Kaluza-Klein excitations of Randall-Sundrum bulk fields, after extra dimensional modulus stabilization, and recalling that Randall-Sundrum bulk/brane interactions yield a very deep solution to the EW hierarchy problem. Start with the theory defined by the following action:

with the bulk field given by:

where generally, the bulk action, with worldsheet-uplift, is given by:

and satisfying:

with a Dirac-Born-Infeld brane interaction term:

which, after integration by parts and upon substituting in our action, we get the Horava-Witten action variant:

Now, the bulk fields manifest themselves to 4-D ‘observers’ as infinite towers of scalars with masses . After change of variables to:

our actions reduce to two interaction terms:

and:

where we have