AdS_{d+1} --> AdS_d
  Coset methods are used to construct the action describing the dynamics of the (massive) Nambu-Goldstone scalar degree of freedom associated with the spontaneous breaking of the isometry group of AdS_{d+1} space to that of an AdS_d subspace. The resulting action is an SO(2,d) invariant AdS generalization of the Nambu-Goto action. The vector field theory equivalent action is also determined. 
T.E. Clark, S.T. Love, Muneto Nitta, T. ter Veldhuis