Towards a derivation of holographic entanglement entropy

By H. Casini, M. Huerta, R. Myers. 2011

1,476 citations recorded by the source corpus.

We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to the entanglement entropy is given by A-type trace anomaly for any CFT, without reference to holography.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b001372c8e865149bbe1c50fdede46ce54bfd61a

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. D. Harlow
4. V. Hubeny
5. J. Maldacena
6. T. Nishioka
7. M. Rangamani
8. T. Faulkner

In Nuclear and High Energy Physics

1. R. Myers
2. T. Takayanagi
3. D. Harlow
4. J. Maldacena
5. T. Nishioka
6. V. Hubeny
7. D. Stanford
8. M. Rangamani

In Statistical and Nonlinear Physics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. T. Nishioka
5. V. Hubeny
6. T. Faulkner
7. D. Stanford
8. J. Maldacena

Citations in the corpus

• Holographic geometry of entanglement renormalization in quantum field theories (2012, background): “ tests: the analytical agreements in AdS3/CFT2 [21]; the strong subadditivity [23]; the phase transition when the subsystem Ais disconnected [24]; the agreements of the coefficient of logarithmic terms [21, 25, 26]; moreover, the proof of (1) has been given in [26] when the subregion Ais a round spher”
• Universality of Gravity from Entanglement (2014, background): “Starting from the CFT vacuum state and shifting to a nearly parallel state in the Hilbert space, it is straightforward to show [10, 11] that the variation in δSB in this entanglement entropy can be reexpressed as the variation in a certain energy EB (defined below) associated with the region B.”
• Deriving covariant holographic entanglement (2016, methodology): “This question has been addressed in the AdS/CFT context a long time ago: a prescription to compute real time correlation functions was first given in [19] and was subsequently derived from a Schwinger-Keldysh framework in [20].”
• Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “Moreover, the free energy F on a three-sphere corresponds to a certain entanglement entropy [8].”
• Entanglement entropy from a holographic viewpoint (2012, background): “In the higher dimensional cases, the agreement of q between the AdSd+2 and CFTd+1 has been confirmed in [7, 58, 59, 54] (see also [60–62]).”
• On the architecture of spacetime geometry (2012, background): “For example, this behaviour arises with the HA constructed in [26] for a CFT within a spherical entangling surface and also in the situation where the entangling surface corresponds to a fixed point of some background Killing vector ζ where ∫ Σ ζ = μ μν ν H T d A , e.”
• Causal holographic information (2012, methodology): “This strategy was used in [8] to prove the minimal surface holographic entanglement entropy proposal of [1].”
• Top down approach to 6D SCFTs (2018, background): “In D = 3, there is a related F-theorem [155–157].”
• The constraints of conformal symmetry on RG flows (2011, background): “) The a-anomaly is also closely related to the entanglement entropy across spheres [26,27,28] and it would be very interesting to understand the inequality (1.”
• Shape dependence of entanglement entropy in conformal field theories (2015, neutral): “In conformal field theories, the modular Hamiltonian for a ball-shaped region (of radius R) is also local [4].”
• Exact results for the entanglement entropy and the energy radiated by a quark (2013, background): “Proceeding as in [1], the computation of the entanglement entropy is equal to the thermal entropy in the space ds2S1×Hd−1 = 1 r2 ds(2).”
• Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, background): “A similar construction is also possible for spherical subregions in conformal field theories [2], for null slabs in the case where the vacuum state is defined with respect to the generator of null translations on a null hypersurface [3, 4] etc.”
• Entanglement Entropy of Black Holes (2011, background): “The result (299), as is shown in [39, 181], generalizes to a spherical entangling surface in a conformally-flat spacetime of any even dimension.”
• Emergent Gravity and the Dark Universe (2016, background): “In this way it was proven [10, 11] that the entanglement entropy indeed obeys (1), when the vacuum state is divided into two parts separated by a Killing horizon.”
• Extremal surfaces as bulk probes in AdS/CFT (2012, background): “Similarly, the entanglement entropy [32],[33] associated to a given region A in the boundary is related to the area of a co-dimension 2 extremal(5) surface ending on ∂A.”