  We construct consistent brane-world Kaluza-Klein reductions involving the
radion mode that measures the separation of the domain-wall branes. In these
new examples, we can obtain matter supermultiplets coupled to supergravity on
the brane, starting from pure gauged supergravity in the higher dimension. This
contrasts with previously-known examples of consistent brane-world reductions
involving the radion, where either pure supergravity reduced to pure
supergravity, or else supergravity plus matter reduced to supergravity plus
matter. As well as considering supersymmetric reductions, we also show that
there exist broader classes of consistent reductions of bosonic systems. These
include examples where the lower-dimensional theory has non-abelian Yang-Mills
fields and yet the scalar sector has a potential that admits Minkowski
spacetime as a solution. Combined with a sphere reduction to obtain the
starting point for the brane-world reduction, this provides a Kaluza-Klein
mechanism for obtaining non-abelian gauge symmetries from the geometry of the
reduction, whilst still permitting a Minkowski vacuum in the lower dimension.
