Entanglement Entropy at Large Central Charge

By Thomas Hartman. 2013

454 citations recorded by the source corpus.

Two-dimensional conformal field theories with a large central charge and a small number of low-dimension operators are studied using the conformal block expansion. A universal formula is derived for the Renyi entropies of N disjoint intervals in the ground state, valid to all orders in a series expansion. This is possible because the full perturbative answer in this regime comes from the exchange of the stress tensor and other descendants of the vacuum state. Therefore, the Renyi entropy is related to the Virasoro vacuum block at large central charge. The entanglement entropy, computed from the Renyi entropy by an analytic continuation, decouples into a sum of single-interval entanglements. This field theory result agrees with the Ryu-Takayanagi formula for the holographic entanglement entropy of a 2d CFT, applied to any number of intervals, and thus can be interpreted as a microscopic calculation of the area of minimal surfaces in 3d gravity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1321f3e733bd40640775a08715066c4cd814a4e5

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

In Nuclear and High Energy Physics

1. D. Harlow
2. Thomas Hartman
3. Eric Perlmutter
4. R. Myers
5. T. Takayanagi
6. T. Faulkner
7. J. Maldacena
8. S. Raju

Citations in the corpus

• Information radiation in BCFT models of black holes (2019, methodology): “ographic BCFTs, the correlator of twists on the UHP can be explicitly evaluated [47], using vacuum block dominance and an appropriate sparsity condition on the density of states, in a similar vein to [48]. Using this correlator and the replica trick, the entanglement entropy of the interval A= (1 ;w”
• Holographic entanglement beyond classical gravity (2013, background): “The Ryu-Takayanagi proposal has very recently been proven in detail for certain 1+1 dimensional conformal field theories with large central charge [4, 5], while strong arguments for its validity in higher dimensions have also been presented [6].”
• Holographic entanglement entropy for general higher derivative gravity (2013, background): “al region under consideration in the eld theory. This prescription was conjectured by Ryu and Takayanagi [5] and proven by Lewkowycz and Maldacena [7]. Proof of the formula for special cases includes [6,18,19]. Earlier attempts to prove the formula include [20,21]. One-loop corrections were analyzed”
• 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.”
• Witten diagrams revisited: the AdS geometry of conformal blocks (2015, result): “The ideas developed in this paper originated by thinking about the bulk representation of Virasoro conformal blocks in AdS3/CFT2, based on recent results in this direction [28–33].”
• Bounding the space of holographic CFTs with chaos (2016, methodology): “(33)In contrast, entanglement entropy in the vacuum is not directly related to λL: while the Ryu-Takayanagi result for intervals in vacuum follows from sparseness and a mild assumption about large c growth of OPE coefficients [62], λL = 2π/β does not.”
• Universal spectrum of 2d conformal field theory in the large c limit (2014, background): “Most of the entanglement calculations rely on a small interval expansion, but our results do not, so this rules out the possibility of missing saddlepoints in the second Renyi entropy discussed in [12, 17].”
• Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “tremal surface no longer lies in any preferred bulk slice. The RT/HRT proposal has passed many nontrivial checks, especially for AdS 3=CFT 2, where both sides can be computed explicitly in many cases [124,125]. It also obeys nontrivial properties of entropy like strong-subadditivity [123,126]. Indee”
• Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects (2013, background): “bout EE, including whether EE can count of degrees of freedom in arbitrary d[12,13]. Compelling evidence in support of RT’s conjecture continues to accumulate [25], including rigorous proofs for d= 2 [26,27]. Casini, Huerta, and Myers (CHM) [9] also provided a proof in some special cases, as we now ”
• Multiboundary wormholes and holographic entanglement (2014, methodology): “ture is related to the original moduli in this nontrivial way. It would be very interesting to derive the temperature (3.23) directly from the bulk path integral, perhaps using the technology of e.g. [48,49].12 Applying the same reasoning to the 3-boundary phase transition of section2.3from the conn”
• Relative entropy and holography (2013, background): “It is intriguing that Renyi entropies [22, 23] for these same configurations do not separate into the contributions of A and B to this same order in N , for d = 2 [18, 25] or higher dimensions [56].”
• Semiclassical Virasoro blocks from AdS3 gravity (2015, background): “two-interval Rényi entropies [44,45] – would be very interesting.”