How not to establish the non-renormalizability of gravity

TL;DR

This paper critiques the use of the Bekenstein-Hawking entropy formula in arguments about the non-renormalizability of gravity, highlighting issues with semi-classical extrapolations and dimensional reduction scenarios.

Contribution

It challenges the validity of entropy-based arguments against the possibility of a non-perturbatively renormalizable quantum gravity theory.

Findings

Dimensional reduction scenarios can cause Bekenstein-Hawking entropy to diverge.

Semi-classical extrapolations often rely on problematic assumptions.

The entropy argument may not reliably dismiss the renormalizability of gravity.

Abstract

General relativity cannot be formulated as a perturbatively renormalizable quantum field theory. An argument relying on the validity of the Bekenstein-Hawking entropy formula aims at dismissing gravity as non-renormalizable per se, against hopes (underlying programs such as Asymptotic Safety) that d-dimensional GR could turn out to have a non-perturbatively renormalizable d-dimensional quantum field theoretic formulation. In this note we discuss various forms of highly problematic semi-classical extrapolations assumed by both sides of the debate concerning what we call The Entropy Argument, and show that a large class of dimensional reduction scenarios leads to the blow-up of Bekenstein-Hawking entropy.