Domain walls with localized gravity and domain-wall/quantum field theory correspondence

We review general domain-wall solutions supported by a delta-function source, together with a single pure exponential scalar potential in supergravity. These scalar potentials arise from a sphere reduction in M theory or string theory. There are several examples of flat (BPS) domain walls that lead to a localization of gravity on the brane, and for these we obtain the form of the corrections to Newtonian gravity. These solutions are lifted back on certain internal spheres to $D=11\mathrm{}$ and $D=10\mathrm{}$ as M-branes and D-branes. We find that the domain walls that can trap gravity yield M-branes or Dp-branes that have a natural decoupling limit, i.e., $p<~5,$ with the delta-function source providing an ultraviolet cutoff in a dual quantum field theory. This suggests that the localization of gravity can generally be realized within a domain-wall/QFT correspondence, with the delta-function domain-wall source providing a cutoff from the space-time boundary for these domain-wall solutions. We also discuss the form of the one-loop corrections to the graviton propagator from the boundary QFT that would reproduce the corrections to the Newtonian gravity on the domain wall.