Radius stabilization and brane running in the Randall-Sundrum type 1 model

We study the effective potential of a scalar field based on the 5D gauged supergravity for the Randall-Sundrum type one brane model in terms of the brane running method. The scalar couples to the brane such that the Bogomolnyi-Prasad-Sommerfield conditions are satisfied for the bulk configuration. The resulting effective potential implies that the interbrane distance is undetermined in this case, and we need a small Bogomolnyi-Prasad-Sommerfield breaking term on the brane to stabilize the interbrane distance at a finite length. We also discuss the relationship to the Goldberger-Wise model.