Entanglement entropy for the n-sphere
By S. C. Bariloche, Ŕ. Negro. 2010
174 citations recorded by the source corpus.
Abstract We calculate the entanglement entropy for a sphere and a massless scalar field in any dimensions. The reduced density matrix is expressed in terms of the infinitesimal generator of conformal transformations keeping the sphere fixed. The problem is mapped to the one of a thermal gas in a hyperbolic space and solved by the heat kernel approach. The coefficients of the logarithmic term in the entropy for 2 and 4 spacetime dimensions are in accordance with previous numerical and analytical results. In particular, the four-dimensional result, together with the one reported by Solodukhin, gives support to the Ryu–Takayanagi holographic ansatz. We also find that there is no logarithmic contribution to the entropy for odd spacetime dimensions.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/c10c30a00d6b339887f91f6838e86e35d6fb1c94
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In Astronomy and Astrophysics
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Citations in the corpus
- Distributional Geometry of Squashed Cones (2013, methodology): “Later, for simple geometries in Minkowski spacetime, it was confirmed both by numerical calculations (for a sphere and a cylinder) [7] and by an analytic analysis (for a sphere) [8].”
- Entanglement entropy from a holographic viewpoint (2012, methodology): “Refer to [66, 67, 68, 69, 70, 71] for calculations of q and pd in free field theories.”
- Towards a derivation of holographic entanglement entropy (2011, background): “This construction was, in part, inspired by the appearance of a hyperbolic space in the calculations of entanglement entropies across spheres for a free scalar in [15] and it generalizes some older observations in ref.”
- AdS description of induced higher-spin gauge theory (2013, background): “In even and odd dimensions this then gives [10, 71,79] ∫ volHd+1 = π Γ ( − 2 ) , d odd , 2(−π) Γ(1+ d2) logR , d even , (6.”
- Entanglement Entropy of Black Holes (2011, methodology): “For d > 4 the logarithmic term in the entropy of a round sphere has been calculated by Casini and Huerta [38] directly in Minkowski spacetime.”
- Holographic entanglement entropy in Lovelock gravities (2011, methodology): “Recently, [44] analytically computed the entanglement entropy for the region of a ball in a massless scalar field theory in arbitrary dimensions, further verifying Solodukhin’s formula for this case.”