Hyperspherical entanglement entropy

TL;DR

This paper demonstrates that the coefficient of the logarithmic term in hyperspherical entanglement entropy equals the conformal anomaly, using conformal transformations and heat-kernel coefficients, confirming recent evaluations.

Contribution

It provides an analytical proof linking hyperspherical entanglement entropy to the conformal anomaly through conformal transformations and heat-kernel analysis.

Findings

Coefficient of log term equals conformal anomaly.

Analytical proof confirms recent numerical evaluations.

Conformal transformation relates entanglement entropy to heat-kernel coefficients.

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.