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.