AdS/CFT and strong subadditivity of entanglement entropy
By Tomoyoshi Hirata, T. Takayanagi. 2006
228 citations recorded by the source corpus.
Recently, a holographic computation of the entanglement entropy in conformal field theories has been proposed via the AdS/CFT correspondence. One of the most important properties of the entanglement entropy is known as the strong subadditivity. This requires that the entanglement entropy should be a concave function with respect to geometric parameters. It is a non-trivial check on the proposal to see if this property is indeed satisfied by the entropy computed holographically. In this paper we examine several examples which are defined by annuli or cusps, and confirm the strong subadditivity via direct calculations. Furthermore, we conjecture that Wilson loop correlators in strongly coupled gauge theories satisfy the same relation. We also discuss the relation between the holographic entanglement entropy and the Bousso bound.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/70b5ca6c93a2f9bbd069ceccc129fd1269e808c5
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Citations in the corpus
- AdS bubbles, entropy and closed string tachyons (2006, background): “This follows from the general property of the von-Neumann entropy, which is known as the strong subadditivity [47].”
- Mutual information and the F-theorem (2015, background): “These surfaces have also been considered in the context of holographic entanglement entropy by [53, 72, 76].”
- Holographic entanglement entropy: an overview (2009, background): “Also the direct calculations of the entanglement entropy in the CFT side are very complicated in higher dimensions.”
- Holographic evolution of the mutual information (2011, background): “The proposal of [6, 7] satisfies many properties and also important inequalities of the entanglement entropy (the simplest of them is the strong subadditivity) [10, 11, 12].”
- Entanglement entropy from a holographic viewpoint (2012, background): “The strong subadditivity (7) can also be holographically proven very quickly for the holographic entanglement entropy in static backgrounds [44] (see also [46]).”
- Entanglement as a probe of confinement (2007, background): “. In non-conformal theories, the volume of the 8 − d compact dimensions and the dilaton are in general not constant. A natural generalization of (5) to the corresponding ten dimensional geometries is [1, 7] SA = 1 4G(10) N Z d8σe−2φ q G(8) ind . (6) The entropy is obtained by minimizing theaction (6”
- A covariant holographic entanglement entropy proposal (2007, background): “3) 12 In this case we can easily prove the strong subadditivity of holographic entanglement entropy [25] as in [26] since two minimal surfaces on the same time slice can intersect with each other if they do so at the boundary of AdS.”
- Black Holes, Qubits and Octonions (2008, background): “In particular, as far as we can tell our analogy is unconnected with the work of [206, 207, 208, 209, 210, 211, 212] relating black holes and entanglement entropy in field theory.”
- Bit Threads and Holographic Entanglement (2016, background): “First, the minimal surface can jump under continuous deformations of A [4–7], suggesting that the bits strangely jump from one place to another.”
- Holographic Calculation of Boundary Entropy (2007, background): “The holographic derivation of strong subadditivity has been given in [10, 9].”
- An intuitive proof of the data processing inequality (2011, methodology): “Other approaches have used the operational meaning of the von Neumann entropy [9,10], Minkowski inequalities [11,12], or holographic gravity theory [13,14].”
- Entanglement entropy: Holography and renormalization group (2018, background): “…additional UV divergences whose coefficients depend on the opening angles (Bueno and Myers, 2015; Bueno et al., 2015; Casini and Huerta, 2007; Casini et al., 2009; Elvang and Hadjiantonis, 2015; Fradkin and Moore, 2006; Hirata and Takayanagi, 2007; Klebanov et al., 2012b; Myers and Singh, 2012b).”
- Comments on holographic entanglement entropy and RG flows (2012, methodology): “This implies that with the strip geometry in arbitrary dimensions, we have dĉd/dl ≤ 0 — the same observation was made in [93].”