Quantum Information in Quantum Gravity II

If entanglement entropy in a small geodesic ball is maximized at fixed volume in the vacuum, then it should be stationary under variation to a nearby state. I will show that this stationarity condition is equivalent to the semiclassical Einstein equation. If the matter QFT is not conformal, then the derivation requires a further assumption about QFT, whose validity is currently under investigation. [Based on http://arxiv.org/abs/1505.04753]

In recent years, tensor networks have been proposed as a useful framework for understanding holographic duality, especially the relation between quantum entanglement and space-time geometry. Most tensor networks studied so far are defined in the large scale compared with AdS radius. In this talk, I will describe a new tensor network approach which defines a holographic mapping that applies to a refined network with sub-AdS scale resolution, or even to a flat space. The idea of quantum error correction code plays an essential role in this approach. Using this new tensor network, we can study features of the bulk theory, such as how locality at sub-AdS scale emerges in a "low energy subspace" even though the whole theory is intrinsically nonlocal, as a quantum gravity theory should be.

In a theory of gravity, observables must be diffeomorphism-invariant. Such observables are nonlocal, in contrast with the usual formulation of local quantum field theory. Working to leading order in Newtons constant G, I'll describe a construction of diffeomorphism-invariant observables for a scalar field coupled to gravity that closely parallels an analogous construction for charged particles in electrodynamics. These observables acting on the vacuum create scalar particles together with their (linearized) gravitational dressing. The commutator of two such spacelike-separated observables is nonvanishing at order G, and is related to the gravitational potential between two masses. Based on arXiv:1507.07921 with Steve Giddings.

In the first part of this talk, we discuss a generalized replica trick that is based on replica symmetry breaking partitions. This allows us compute the modular Hamiltonian, relative entropy and quantum Fisher information of excited states in conformal field theory. In the second part, we consider holographic CFTs and show that quantum Fisher metric for ball shaped regions in vacuum is dual to the canonical energy of metric perturbations corresponding to the Rindler wedge of Anti-de Sitter space.