Geometric Flow Description of Minimal Surfaces
arXiv:1910.06680 · doi:10.1103/PhysRevD.101.086015
Abstract
We introduce a description of a minimal surface in a space with boundary, as the world-hypersurface that the entangling surface traces. It does so by evolving from the boundary to the interior of the bulk under an appropriate geometric flow, whose parameter is the holographic coordinate. We specify this geometric flow for arbitrary bulk geometry. In the case of pure AdS spaces, we implement a perturbative approach for the solution of the flow equation around the boundary. We systematically study both the form of the perturbative solution as well as its dependence on the boundary conditions. This expansion is sufficient for the determination of all the divergent terms of the holographic entanglement entropy, including the logarithmic universal terms in odd spacetime bulk dimensions, for an arbitrary entangling surface, in terms of the extrinsic geometry of the latter.
arXiv comment39 pages + 10 pages appendix, 6 figures
References in corpus (46)
- Gauge Theory Correlators from Non-Critical String Theory
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement Entropy and Quantum Field Theory
- Entanglement in quantum critical phenomena
- Aspects of Holographic Entanglement Entropy
- Entropy and Area
- The Holographic Weyl anomaly
- Towards a derivation of holographic entanglement entropy
- Building up spacetime with quantum entanglement
- On Geometric Entropy
- Holographic Entanglement Entropy: An Overview
- Entanglement entropy of black holes
- Entanglement as a Probe of Confinement
- Holographic Entanglement Entropy for General Higher Derivative Gravity
- Entanglement entropy, conformal invariance and extrinsic geometry
- Holographic Evolution of Entanglement Entropy
- Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
- Generalized entropy and higher derivative Gravity
- On Holographic Entanglement Entropy and Higher Curvature Gravity
- Holographic Fermi Surfaces and Entanglement Entropy
- Holographic Entanglement Entropy in Lovelock Gravities
- AdS Bubbles, Entropy and Closed String Tachyons
- Universality of corner entanglement in conformal field theories
- Entanglement Entropy, Trace Anomalies and Holography
- Comments on quantum gravity and entanglement
- Holographic Entanglement Entropy for the Most General Higher Derivative Gravity
- Entanglement entropy in higher derivative holography
- Holographic Entanglement Entropy and Fermi Surfaces
- Some Calculable Contributions to Holographic Entanglement Entropy
- Corner contributions to holographic entanglement entropy
- On Shape Dependence and RG Flow of Entanglement Entropy
- Entanglement Entropy for Singular Surfaces
- Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
- On entanglement entropy functionals in higher derivative gravity theories
- Notes on Euclidean Wilson loops and Riemann Theta functions
- Entanglement Entropy for Probe Branes
- Generalized gravitational entropy of probe branes: flavor entanglement holographically
- Entanglement Entropy for Singular Surfaces in Hyperscaling violating Theories
- Wilson loops and Riemann theta functions II
- Entropy vs Gravitational Action: Do Total Derivatives Matter?
- Entanglement entropy and differential entropy for massive flavors
- Entropy discrepancy and total derivatives in trace anomaly
- Non-conformal entanglement entropy
- Static Elliptic Minimal Surfaces in AdS(4)
- On the Holographic Entanglement Entropy for Non-smooth Entangling Curves in AdS(4)