Quantum Holographic Entanglement Entropy to All Orders in Expansion
arXiv:1911.01640 · doi:10.1093/ptep/ptaa019
Abstract
We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the Wheeler-DeWitt equation, we compute quantum corrections to the holographic entanglement entropy for a circular entangling surface on the boundary three sphere. Similarly to our previous work on the sphere partition function, the path integrals are dominated by a replica version of asymptotically AdS conic geometries at saddle points. As expected from a general CFT argument, the final result is minus the free energy on the three sphere which agrees with the logarithm of the Airy partition function for the ABJM theory that sums up all perturbative corrections despite the absence of supersymmetries. The all-order holographic entanglement entropy cleanly splits into two parts, (1) the -corrected Ryu-Takayanagi minimal surface area and (2) the bulk entanglement entropy across the minimal surface, as suggested in the earlier literature. It is explicitly shown that the former comes from the localized conical singularity of the replica geometries and the latter from the replication of the bulk volume.
arXiv comment23 pages, 6 figures
References in corpus (44)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- The World as a Hologram
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- A Stress Tensor for Anti-de Sitter Gravity
- Wilson loops in large N field theories
- A Covariant Holographic Entanglement Entropy Proposal
- Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
- Eternal Black Holes in AdS
- Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
- Towards a derivation of holographic entanglement entropy
- Generalized gravitational entropy
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Holographic Entanglement Entropy: An Overview
- Surface Terms as Counterterms in the AdS/CFT Correspondence
- On the Holographic Renormalization Group
- Entanglement entropy in free quantum field theory
- Fractional M2-branes
- From weak to strong coupling in ABJM theory
- Black hole microstates in AdS from supersymmetric localization
- The Conical Singularity And Quantum Corrections To Entropy Of Black Hole
- ABJM theory as a Fermi gas
- Nonperturbative aspects of ABJM theory
- Non-perturbative effects and the refined topological string
- Summing Up All Genus Free Energy of ABJM Matrix Model
- Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
- Instanton Effects in ABJM Theory from Fermi Gas Approach
- Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals
- Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual
- Entanglement entropy for the n-sphere
- Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
- Instanton Bound States in ABJM Theory
- D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades
- Anomalous radius shift in AdS(4)/CFT(3)
- Supersymmetric Renyi Entropy
- Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
- Localization in Supergravity and Quantum Holography
- Sphere partition functions and cut-off AdS
- Exact ABJM Partition Function from TBA
- The Gravity Dual of Supersymmetric Renyi Entropy
- Airy Function and 4d Quantum Gravity