Localizing Information in Quantum Gravity and State-dressed Local Operators in AdS/CFT

It is well known that quantum information can be strictly localized in quantum field theory. Similarly, one can also localize information in classical gravity up to quantities like the ADM mass which are fixed by the constraints of general relativity. On the other hand, the holographic nature of quantum gravity suggests that information can never be localized deep inside some spacetime region, and is always accessible from the boundary. This is meant to hold as a non-perturbative statement and it remains to be understood whether quantum information can be localized within G_N perturbation theory. In this talk, I will address this problem from the point of view of the AdS/CFT correspondence. I will construct candidate local operators that can be used to localize information deep inside the bulk. They have the following two properties: they act just like standard HKLL operators to leading order at large N, but commute with the CFT Hamiltonian to all orders in 1/N. These operators can only be constructed in a particular class of states which have a large energy variance, for example coherent states corresponding to semi-classical geometries. The interpretation of these operators is that they are dressed with respect to a feature of the state, rather than to the boundary. I will comment on connections with black holes and computations of the Page curve.

Zoom link: https://pitp.zoom.us/j/94678968773?pwd=NUJhOEJmRWxLa3pCVUtVVi9DdkE3QT09