Stability of RS brane for tachyonic scalars

We study the stability of the RS brane embedded in the AdS$_5$ vacuum of 5d gauged supergravity, where many tachyonic scalars exist. We consider a model in which these scalars couple to the brane such that the BPS conditions are satisfied to preserve the bulk supersymmetric configuration. In this case, we find that these tachyons are not trapped on the brane and only the massless dilaton is localized. As a result, the braneworld is stable. Further, the effective action of trapped fields is studied by using the brane running method developed recently, and we find that the action is independent of the brane position.