A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections
arXiv:1902.10161 · doi:10.1007/JHEP06(2019)059
Abstract
We use the formalism of geodesic Witten diagrams to study the holographic realization of the conformal block expansion for entanglement entropy of two disjoint intervals. The agreement between the Ryu-Takayanagi formula and the identity block contribution has a dual realization as the product of bulk to boundary propagators. Quantum bulk corrections instead arise from stripped higher order diagrams and back-reaction effects; these are also mapped to the structure for terms found in \cite{Faulkner:2013ana}, with the former identified as the bulk entanglement entropy across the Ryu-Takayanagi surfaces. An independent derivation of this last statement is provided by implementing a twist-line formalism in the bulk, and additional checks from the computation of mutual information and single interval entanglement entropy. Finally an interesting correspondence is found between the recently proposed holographic entanglement of purification, and an approximated form for certain Renyi entropies corrections.
25 pages, v3: subsection 3.1 and some clarifications have been added. Matches the version to be published on JHEP
References in corpus (9)
- Towards a derivation of holographic entanglement entropy
- Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
- Entanglement entropy of two disjoint intervals in conformal field theory II
- supersymmetric indices and the four-dimensional A-model
- Entanglement Entropy at Large Central Charge
- The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
- Holographic dual of the five-point conformal block
- Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
- A perturbative study on the analytic continuation for generalized gravitational entropy