A covariant holographic entanglement entropy proposal

By V. Hubeny, M. Rangamani, T. Takayanagi. 2007

2,262 citations recorded by the source corpus.

With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5c449897c6813c5c1edff88d873d7842db9ee07e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. R. Myers
2. T. Takayanagi
3. D. Harlow
4. D. Stanford
5. T. Nishioka
6. Thomas Hartman
7. S. Raju
8. S. Shenker

In Nuclear and High Energy Physics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. S. Raju
5. D. Stanford
6. J. Maldacena
7. Thomas Hartman
8. V. Hubeny

In Statistical and Nonlinear Physics

1. R. Myers
2. D. Harlow
3. S. Raju
4. D. Stanford
5. T. Takayanagi
6. J. Maldacena
7. Thomas Hartman
8. V. Hubeny

Citations in the corpus

• On volumes of subregions in holography and complexity (2016, methodology): “• For a given time t on the boundary and an entangling region A, find the codim-two HRT surface [23].”
• Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, methodology): “Our ideal candidate for a formula for holographic entanglement entropy in a nonclassical bulk should therefore (1) be sensitive to quantum effects at any order in ~, (2) reproduce the classical HRT formula at O(~−1), and (3) reproduce the result of FLM at O(~0).”
• The AdS/CFT correspondence (2014, methodology): “FT: whilst we understand a great deal of the spacetime outside the horizon, encoding the region inside is far more subtle. Entanglement and geometry: The proposals of holographic entanglement entropy [51,54] suggest a mysterious connection between entanglement and geometry. This has been followed by”
• Gravity and hydrodynamics: lectures on the fluid-gravity correspondence (2009, methodology): “vour of quasi-local horizons comes from the analysis of holographic entanglement entropy (for specified regions on the boundary) in time dependent states of the dual field theory, see the discussion in [99]. 40As explained in [60] we use the term apparent horizon to denote a co-dimension one surface i”
• Lessons from the information paradox (2020, methodology): “The entanglement entropy between these regions, S(R), can be computed using – 78 – the standard RT/HRT formula in the bulk.”
• Islands in asymptotically flat 2D gravity (2020, background): “Recent proposed generalizations of this formula define an ‘island rule entropy’ for time-dependent evaporating black holes in AdS - and even for those in flat space - involving a ‘quantum extremal surface’ or QES [8–10].”
• Random Quantum Circuits (2022, background): “Physical review letters, 55(26):2924, 1985.”
• Entropy, extremality, euclidean variations, and the equations of motion (2017, background): “Furthermore, it is valid in general time-dependent cases [10, 11].”
• Holographic local quenches and entanglement density (2013, methodology): “This minimizing procedure nicely matches with the HEE formula (3.1) as pointed out in [40].”
• Complexity and Shock Wave Geometries (2014, methodology): “The construction involved connecting the boundaries by (D − 2)-dimensional surfaces similar to the Ryu-Takayanagi surfaces [16][17] used by Hartman and Maldacena”
• Entanglement and correlation functions following a local quench: a conformal field theory approach (2007, background): “The most common situation studied so far concerns a sudden quench of some coupling of the model Hamiltonian [6]– [10].”
• Extremal surfaces as bulk probes in AdS/CFT (2012, methodology): “5 As argued in [34], such extremal surface is in fact related to light-sheet constructions of the covariant entropy bound [35] in the bulk spacetime.”
• Relative entropy and holography (2013, methodology): “16) is stationary (but not static), we must apply the covariant prescription suggested by [39] to evaluate the holographic entanglement entropy.”
• Shape dependence of entanglement entropy in conformal field theories (2015, neutral): “We show from a purely field theory calculation that the non-local part of the entanglement density in any CFT is universal, and proportional to the coefficient CT appearing in the two-point function of stress tensors in that CFT.”