Entanglement Renyi entropies in holographic theories

By M. Headrick. 2010

661 citations recorded by the source corpus.

Ryu and Takayanagi conjectured a formula for the entanglement (von Neumann) entropy of an arbitrary spatial region in an arbitrary holographic eld theory. The von Neumann entropy is a special case of a more general class of entropies called R enyi entropies. Using Euclidean gravity, Fursaev computed the entanglement R enyi entropies (EREs) of an arbitrary spatial region in an arbitrary holographic eld theory, and thereby derived the RT formula. We point out, however, that his EREs are incorrect, since his putative saddle points do not in fact solve the Einstein equation. We remedy this situation in the case of two-dimensional CFTs, considering regions consisting of one or two intervals. For a single interval, the EREs are known for a general CFT; we reproduce them using gravity. For two intervals, the RT formula predicts a phase transition in the entanglement entropy as a function of their separation, and that the mutual information between the intervals vanishes for separations larger than the phase transition point. By computing EREs using gravity and CFT techniques, we nd evidence supporting both predictions. We also nd evidence that large-N symmetric-product theories have the same EREs as holographic ones.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/bedd6e2046a56b922947d1045624fa2752d9a085

How researchers see this paper

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

In Astronomy and Astrophysics

1. R. Myers
2. T. Takayanagi
3. V. Hubeny
4. Thomas Hartman
5. T. Faulkner
6. M. Rangamani
7. D. Harlow
8. T. Nishioka

In Nuclear and High Energy Physics

1. R. Myers
2. T. Takayanagi
3. Thomas Hartman
4. V. Hubeny
5. T. Faulkner
6. D. Harlow
7. M. Rangamani
8. Xi Dong

Citations in the corpus

• A Holographic View on Physics out of Equilibrium (2010, positive): “This is indeed supported by the proposal 56 Justification of this remarkable statement was subsequently provided in [210] using replica trick to evaluate entanglement Renyi entropies; although an error in this derivation was recently pointed out by [211], the correction nevertheless gives further ev”
• Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “As emphasized in [1], the transition between the phase without an island and that with the island is nothing more than the usual transition between different classes of RT surfaces [73–75] – see figure 2.”
• A stereoscopic look into the bulk (2016, neutral): “Related formulations have been explored in [42–44].”
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• Virasoro conformal blocks and thermality from classical background fields (2015, positive): “There is also a fascinating connection between conformal blocks and entanglement entropy at large central charge [28] which has recently led to increasingly rich matching of such e(cid:11)ects between gravity and (cid:12)eld theory computations [29, 31{33, 35, 37].”
• Holographic c-theorems in arbitrary dimensions (2010, result): “As emphasized in [75], the derivation presented in [76] is flawed and, for example, leads to incorrect results in holographic calculations of Renyi entropies.”
• Some calculable contributions to holographic entanglement entropy (2011, background): “where v ∼ V indicates that v is a bulk surface that is homologous to the boundary region V [4, 5].”
• A general proof of the quantum null energy condition (2017, background): “These operators are important when replacing non-local twist operators with local operators when viewed from a distance, as in [77–81], or when bringing a twist operator close to an anti-twist operator, as in [34, 82].”
• Holographic mutual information is monogamous (2011, background): “The main evidence for this statement, aside from an extrapolation of the previous line of argument, comes from the results of [4].”
• Entanglement of purification through holographic duality (2017, background): “When A and B are enough far away from each other, the mutual information I(A : B) = S(ρA) + S(ρB)−S(ρAB) is vanishing in the classical gravity limit [21].”
• Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, neutral): “, [110].”
• On volumes of subregions in holography and complexity (2016, background): “g [1–18]) is a measure of the quantum correlations of a quantum state, and is extremely useful in many quantum systems, ranging from condensed matter physics to black hole physics.”
• Time evolution of entanglement entropy from black hole interiors (2013, background): “The configuration in [31] is two disjoint intervals [0, xcross]∪ [1,∞] at fixed time, and the sharp transition appears at xcross = 1 2 .”
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• Entanglement Entropy at Large Central Charge (2013, methodology): “(Note that this is the same as the transformation to the torus in [49, 8]).”