  We study two issues, the localization of various spin fields, and the problem
of the cosmological constant on a brane in five-dimensional anti de Sitter
space. We find that spin-zero fields are localized on a positive-tension brane.
In addition to the localized zero-mode there is a continuous tower of states
with no mass gap. Spin one-half and three-half states can be localized on a
brane with ``negative tension''. Their localization can be achieved on the
positive-tension brane as well, if additional interactions are introduced. The
necessary ingredient of the scenario with localized gravity is the relation
between the bulk cosmological constant and the brane tension. In the absence of
supersymmetry this implies fine-tuning between the parameters of the theory. To
deal with this issue we introduce a four-form gauge field. This gives an
additional arbitrary contribution to the bulk cosmological constant. As a
result, the model gives rise to a continuous family of brane Universe solutions
for generic values of the bulk cosmological constant and the brane tension.
Among these solutions there is one with a zero four-dimensional cosmological
constant.
