Scalar field spacetimes and the anti–de Sitter space/conformal-field theory 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 counterterm prescriptions. The energy associated with the solutions in each case is proportional to $\sqrt{M^2-k^2},$ where M is a constant and k is a scalar charge. In five spacetime dimensions, the counterterm prescription gives an additional vacuum (Casimir) energy, which agrees with that found in the context of AdS conformal-field theory (CFT) correspondence. We find a surprising degeneracy: the energy of the “extremal” scalar field solution $M=k$ equals the energy of global AdS. This result is discussed in light of the AdS/CFT conjecture.