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Actions governing the dynamics of the Nambu-Goldstone modes resulting fromthe spontaneous breaking of the SO(4,2) and $SU(2,2|1)$ isometries of fivedimensional anti-de Sitter space ($AdS_{5}$) and SUSY $AdS_{5}\times S_1$spaces respectively due to a restriction of the motion to embedded fourdimensional $AdS_{4}$ space and four dimensional Minkowski space ($M_4$) probebranes are presented. The dilatonic Nambu-Goldstone mode governing the motionof the $M_4$ space probe brane into the covolume of the SUSY $AdS_5\times S_1$space is found to be unstable. No such instablility appears in the other cases.Gauging these symmetries leads to an Einstein-Hilbert action containing, inaddition to the gravitational vierbein, a massive Abelian vector field coupledto gravity.Comment: 6 pages, 0 figures, to appear in Proceedings of IRGAC 2006: 2nd  International Conference on Quantum Theories and Renormalization Group in  Gravity and Cosmology, Barcelon

Dynamics of (SUSY) AdS space isometry breaking