Entanglement entropy, conformal invariance and extrinsic geometry
By S. Solodukhin. 2008
347 citations recorded by the source corpus.
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface Σ that separates two subsystems of quantum strongly coupled N=4SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a closed-form expression for the entanglement entropy in flat space–time when Σ is sphere S2 and when Σ is two-dimensional cylinder. The contribution of the type A conformal anomaly to entanglement entropy is always determined by topology of surface Σ while the dependence of the entropy on the extrinsic geometry of Σ is due to the type B conformal anomaly.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/25b0148b699365b7898116afafb79c27b6b18c1f
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
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Towards a derivation of holographic entanglement entropy (2011, methodology): “A generalization of the replica trick [12] has been applied to relate entanglement entropy to the trace anomaly for CFT’s in an even number of spacetime dimensions [5, 17].”
- Holographic c-theorems in arbitrary dimensions (2010, background): “One approach refers to the trace anomaly which is fixed by the central charge c for two-dimensional CFT’s [2], i.e., 〈T aa 〉 = − c 12 R .”
- 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 entanglement entropy in Lovelock gravities (2011, methodology): “Independent evidence in support of the work of [26] was first given in [43].”
- Holographic geometry of entanglement renormalization in quantum field theories (2012, methodology): “The holographic formula (1) has passed many tests: the analytical agreements in AdS3/CFT2 [21]; the strong subadditivity [23]; the phase transition when the subsystem A is disconnected [24]; the agreements of the coefficient of logarithmic terms [21, 25, 26]; moreover, the proof of (1) has been give”
- Entanglement Entropy of Black Holes (2011, methodology): “On the other hand, in the absence of rotational symmetry i) there may appear terms in the entropy that are “missing” in the naively applied conical space approach: the extrinsic curvature contributions [204] or even some curvature terms [134].”
- Holographic entanglement entropy for general higher derivative gravity (2013, background): “the holographic entanglement entropy for Gauss-Bonnet gravity leads to the correct universal terms expected for a generic 4-dimensional CFT [13], including extrinsic curvature terms rst worked out in [36]. Other discussions on holographic entanglement entropy in Lovelock gravity include [37,38]. A r”
- 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.”
- Geometric entropy and edge modes of the electromagnetic field (2015, background): “In a conformal field theory, the entanglement entropy of a spherical region has a universal logarithmic divergence, whose coefficient is related to the trace anomaly [42, 43].”