Non-standard compactifications with mass gaps and Newton's law

The four-dimensional Minkowski space-time is considered as a three-brane em bedded 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 fi nd a zero-mode representing the massless graviton in four-dimensional space -time. The novelty of our models is that the graviton spectrum has a genuin e 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 br ane that includes the massless graviton mode is well defined. The gravitati onal force between point particles deviates from the Newton law by Yukawa-t ype corrections, which we compute explicitly. We show that the parameters o f our solutions can be chosen such that these corrections lie within experi mental bounds.