  The four-dimensional Minkowski space-time is considered as a three-brane
embedded in five dimensions, using solutions of five-dimensional supergravity.
These backgrounds have a string theoretical interpretation in terms of D3-brane
distributions. By studying linear fluctuations of the graviton we find a
zero-mode representing the massless graviton in four-dimensional space-time.
The novelty of our models is that the graviton spectrum has a genuine mass gap
(independent of the position of the world-brane) above the zero-mode or it is
discrete. Hence, an effective four-dimensional theory on a brane that includes
the massless graviton mode is well defined. The gravitational force between
point particles deviates from the Newton law by Yukawa-type corrections, which
we compute explicitly. We show that the parameters of our solutions can be
chosen such that these corrections lie within experimental bounds.
