Hyperspherical entanglement entropy

Abstract

The coefficient of the log term in the entanglement entropy associated with hyperspherical surfaces in flat space-time is shown to equal the conformal anomaly by conformally transforming Euclideanised space--time to a sphere and using already existing formulae for the relevant heat--kernel coefficients after cyclic factoring. The analytical reason for the result is that the conformal anomaly on the lune has an extremum at the ordinary sphere limit. A proof is given. Agreement with a recent evaluation of the coefficient is found.

7 pages. Final revision. Historical comments amended. Minor remarks added

References in corpus (4)

• Entanglement entropy in free quantum field theory
• Entanglement entropy, conformal invariance and extrinsic geometry
• Numerical determination of entanglement entropy for a sphere
• Geometric Entropy and Hagedorn/Deconfinement Transition

Cited by in corpus (6)

• Entanglement entropy of black holes
• Distributional Geometry of Squashed Cones
• Numerical determination of the entanglement entropy for free fields in the cylinder
• Finite entanglement entropy from the zero-point-area of spacetime
• On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
• Universal terms of the entanglement entropy in a static closed universe