Newton constant, contact terms and entropy

TL;DR

The paper analyzes how quantum fields renormalize the Newton constant and how this renormalization relates to black hole entropy via entanglement entropy, emphasizing contact terms from gauge fields and gravitons.Using a heat-kernel framework and replica methods, it extends the analysis to massive vectors, $p$-forms, and spin-$2$ gravitons, detailing the operators that govern perturbations and the resulting contributions to $1/G(\epsilon)$ and the conical/entanglement entropies.It shows that entanglement entropy and the Newton constant renormalization align for non-mediator fields, but gauge mediators introduce contact terms that complicate a direct equality; it then proposes a mechanism in which a suitable choice of the bare Newton constant can yield $S_{BH} = S_{ent}$ by canceling non-statistical pieces.The work also highlights that orbifold and $n$-fold cover replica constructions need not be analytically related, especially for higher spins, and discusses the implications for the universality of BH 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).