Supersymmetry and the brane world

We investigate the possibility of gravity localization on the brane in the context of supersymmetric theories. To realize this scenario one needs to f ind a theory with the supersymmetric ow stable in IR at two critical points , one with positive and the other with negative values of the superpotentia l. We perform a general study of the supersymmetric ow equations of gauged massless supergravity interacting with arbitrary number of vector multiplet s and demonstrate that localization of gravity does not occur. The same con clusion remains true when tensor multiplets are included. We analyze all re cent attempts to find a BPS brane-world and conclude that localization of g ravity on the brane in supersymmetric theories remains a challenging but un solved problem.