Bulk reconstruction and the Hartle-Hawking wavefunction

TL;DR

This paper explores the relationship between bulk observable state dependence and diffeomorphism invariance in gauge/gravity duality, proposing a framework where the bulk-to-boundary map remains linear across the entire Hilbert space.

Contribution

It introduces a Hartle-Hawking formulation to address nonperturbative IR issues, ensuring a linear bulk-to-CFT map even with constraints like the black hole information paradox.

Findings

Bulk constraints obstruct linear maps in perturbation theory.

Hartle-Hawking wavefunctions resolve nonperturbative IR issues.

The bulk-to-boundary map is linear on the full Hilbert space.

Abstract

In this work, a relation is found between state dependence of bulk observables in the gauge/gravity correspondence and nonperturbative diffeomorphism invariance. Certain bulk constraints, such as the black hole information paradox, appear to obstruct the existence of a linear map from bulk operators to exact CFT operators that is valid over the entire expected range of validity of the bulk effective theory. By formulating the bulk gravitational physics in the Hartle-Hawking framework to address these nonperturbative IR questions, I will demonstrate, in the context of eternal AdS-Schwarzschild, that the problematic operators fail to satisfy the Hamiltonian constraints nonperturbatively. In this way, the map between bulk effective theory Hartle-Hawking wavefunctions and exact CFT states can be linear on the full Hilbert space.