Scalar field spacetimes and the AdS/CFT conjecture

TL;DR

This paper explores scalar field spacetimes in asymptotically AdS spaces, calculating conserved charges and revealing a surprising energy degeneracy that relates to the AdS/CFT correspondence.

Contribution

It introduces a class of scalar field solutions in AdS spacetimes and analyzes their conserved charges, highlighting a novel energy degeneracy relevant to AdS/CFT.

Findings

Energy proportional to √(M² - k²) in various dimensions

Counter-term prescription yields Casimir energy in 5D

Degeneracy where extremal solution energy equals pure AdS

Abstract

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 $\sqrt{M^2 - k^2}$, 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 result is discussed in light of the AdS/CFT conjecture.