Ja n 20 01 Scalar field spacetimes and the AdS / CFT conjecture

We describe a class of asymptotically AdS scalar field spacetimes, and calculate the associated conserved charges for three, four and five spacetime dimensions using the conformal and counter-term prescriptions. The energy associated with the solutions in each case is proportional to √ M 2 − k 2 , where M is a constant and k is a scalar charge. In five spacetime dimensions, the counter-term prescription gives an additional vacuum (Casimir) energy, which agrees with that found in the context of AdS/CFT correspondence. We find a surprising degeneracy: the energy of the " extremal " scalar field solution M = k equals the energy of pure AdS. This suggests that two distinct spacetimes correspond to the boundary Yang-Mills theory vacuum in AdS/CFT correspondence.