Nonlinear realization of local symmetries of AdS space

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local symmetries of AdS{sub d+1} space due to the embedding of an AdS{sub d} brane. The resulting action is an SO(2,d) invariant AdS form of the Einstein-Hilbert action, which in addition to the AdS{sub d} gravitational vielbein, also includes a massive vector field localized on the brane. Its long wavelength dynamics is the same as a massive Abelian vector field coupled to gravity in AdS{sub d} space.