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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.

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.