  We address the renormalized effective action for a Randall-Sundrum brane
running in 5d bulk space. The running behavior of the brane action is obtained
by shifting the brane-position without changing the background and the
fluctuations. After an appropriate renormalization, we obtain an effective, low
energy braneworld action, in which the effective 4d Planck mass is independent
of the running-position. We address some implications of this effective action.
