Newton constant, contact terms and entropy

TL;DR

This paper examines how various quantum fields affect the renormalization of the Newton constant and explores their implications for black hole entropy and entanglement entropy, addressing contact terms and non-analyticities in entropy calculations.

Contribution

It extends the analysis of contact terms in Newton constant renormalization to massive vector fields, p-forms, and spin-2 particles, and proposes a mechanism linking Bekenstein-Hawking entropy with entanglement entropy.

Findings

Contact terms originate from interaction-mediating fields.

Non-analytic entropy terms are explained by construction differences.

A mechanism links Bekenstein-Hawking and entanglement entropy.

Abstract

We discuss the renormalization of the Newton constant due to fields of various spin $s$. We first briefly review the cases of $s=0, \, 1/2, \, 1,\, 3/2$ already discussed in the literature and notice the appearance of the well-known contact terms for the vector bosons. We then extend this discussion of the contact terms to massive vector fields, $p$-forms and to the case of spin $s=2$ particles (gravitons). We observe that, in general, the contact terms originate from the fields which mediate the interactions (such as vector gauge bosons and gravitons). We then discuss entanglement entropy and the conical entropy and their relation to the renormalized Newton constant. We address the puzzle of the non-analytic terms due to fields of spin $s=2$ and suggest that the resolution of this puzzle comes from the non-equivalence of the orbifold and $n$-fold cover constructions which are used in the entropy calculations. Finally, we propose a mechanism by which the Bekenstein-Hawking entropy is identified with entanglement entropy in any theory which includes both matter fields and the mediators of interactions (vector gauge bosons and gravitons).