Short-distance regularity of Green's function and UV divergences in entanglement entropy

TL;DR

This paper demonstrates that in quantum field theories, the entanglement entropy remains UV divergent regardless of how regular the Green's function's short-distance behavior is, emphasizing the universal nature of these divergences.

Contribution

It clarifies that regularity of Green's functions at short distances does not eliminate UV divergences in entanglement entropy, providing a detailed analysis and calculation of the leading divergence.

Findings

Entanglement entropy is always UV divergent regardless of Green's function regularity.

Regular Green's functions do not remove UV divergences in entanglement entropy.

Calculated the leading divergent term in a specific regular Green's function scenario.

Abstract

Reformulating our recent result (arXiv:1007.1246 [hep-th]) in coordinate space we point out that no matter how regular is short-distance behavior of Green's function the entanglement entropy in the corresponding quantum field theory is always UV divergent. In particular, we discuss a recent example by Padmanabhan (arXiv:1007.5066 [gr-qc]) of a regular Green's function and show that provided this function arises in a field theory the entanglement entropy in this theory is UV divergent and calculate the leading divergent term.