  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.
