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We consider the relative entropy between the vacuum state and a state obtained by applying an exponentiated stress tensor to the vacuum of a chiral conformal field theory on the lightray. The smearing function of the stress tensor can be viewed as a vector field on the real line generating a diffeomorphism. We show that the relative entropy is equal to $c$ times the so-called Schwarzian action of the diffeomorphism. As an application of this result, we obtain a formula for the relative entropy between the vacuum and a solitonic state.
We show that the relative entropy between the reduced density matrix of the vacuum state in some region $A$ and that of an excited state created by a unitary operator localized at a small distance $ell$ of a boundary point $p$ is insensitive to the g
We parametrize the (2+1)-dimensional AdS space and the BTZ black hole with Fefferman-Graham coordinates starting from the AdS boundary. We consider various boundary metrics: Rindler, static de Sitter and FRW. In each case, we compute the holographic
We propose a new non-holographic formulation of AdS/CFT correspondence, according to which quantum gravity on AdS and its dual non-gravitational field theory both live in the same number D of dimensions. The field theory, however, appears (D-1)-dimen
Recent work has demonstrated the need to include contributions from entanglement islands when computing the entanglement entropy in QFT states coupled to regions of semiclassical gravity. We propose a new formula for the reflected entropy that includ
These lectures review recent developments in our understanding of the emergence of local bulk physics in AdS/CFT. The primary topics are sufficient conditions for a conformal field theory to have a semiclassical dual, bulk reconstruction, the quantum