How not to establish the non-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.

17 pages

References in corpus (3)

• Thermodynamics of photons on fractals
• Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations
• Asymptotic Safety, Asymptotic Darkness, and the hoop conjecture in the extreme UV

Cited by in corpus (2)

• Renormalizability of alternative theories of gravity: differences between power counting and entropy argument
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment