Wheeler-DeWitt equation and AdS/CFT correspondence

The radial Wheeler-DeWitt equation on the asymptotically AdS spacetime proposed in Freidel [10] has as its semiclassical solution the wave function that asymptotically satisfies the conformal Ward identity, exemplifying the AdS/CFT correspondence. In this Letter we show that this result holds also in the case of a complete quantum solution of the radial Wheeler-DeWitt equation. It turns out that if the wave function is expanded in the parameter ρ with ρ→0 defines the asymptotic boundary of the spacetime, the quantum loop corrections to the semiclassical wave are of subleading order.