Wheeler-De Witt equation and AdS/CFT correspondence

TL;DR

This paper demonstrates that the quantum solution to the radial Wheeler-De Witt equation in asymptotically AdS spacetimes aligns with the AdS/CFT correspondence, extending previous semiclassical results to the full quantum level.

Contribution

It shows that quantum loop corrections are subleading, confirming the robustness of the AdS/CFT correspondence at the quantum level in this context.

Findings

Quantum solutions match semiclassical conformal Ward identities.

Quantum loop corrections are subleading as boundary is approached.

Results extend AdS/CFT correspondence to full quantum solutions.

Abstract

The radial Wheeler--De Witt equation on the asymptotically AdS spacetime proposed in [9] has as its semiclassical solution the wave function that asymptotically satisfies the conformal Ward identity, exemplifying the AdS/CFT correspondence. In this paper we show that this results holds also in the case of a complete quantum solution of the radial Wheeler--De Witt equation. It turns out that if the wavefunction is expanded in the parameter $\rho$ with $\rho\rightarrow0$ defines the asymptotic boundary of the spacetime, the quantum loop corrections to the semiclassical wave are of subleading order.