Effective action and brane running

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.