Supersymmetric Domain-Wall World from D=5 Simple Gauged Supergravity

We provide explicit examples of supersymmetric domain walls of a five-dimensional simple (N=2, U(1)) gauged supergravity theory constructed by Gunaydin, Townsend and Sierra. These conformally flat solutions interpolate between supersymmetric isolated anti-deSitter vacua, satisfy the Killing spinor (first order) differential equations, have the energy density related to the cosmological constants of the isolated supersymmetric vacua, and the four-dimensional world on the domain wall is a flat world with N=1 supersymmetry. A analysis of such solutions is given for the example of one (real, neutral) vector supermultiplet with the most general form of the prepotential. As the gauge coupling becomes very large (compared to five-dimensional Planck constant), these domain walls become infinitely thin, and a special case of a $Z_2$ symmetric domain wall is a supersymmetric realization of the static domain wall solution considered by Randall and Sundrum.