Brane world effective action at low energies and AdS/CFT correspondence

A low energy iteration scheme to study nonlinear gravity in the brane world is developed. As a result, we obtain the brane world effective action at low energies. The relation between the geometrical approach and the approach using the AdS/CFT correspondence is also clarified. In particular, we find generalized dark radiation as homogeneous solutions in our iteration scheme. Moreover, the precise correspondence between the bulk geometry and the brane effective action is established, which gives a holographic view of the brane world.