Renormalization and causality violations in classical gravity coupled with quantum matter

TL;DR

This paper demonstrates that classical gravity coupled with quantum matter can be renormalized with a finite set of couplings, but it leads to high-energy causality violations, linking acausal gravity to higher-derivative gravity.

Contribution

It introduces a renormalizable model of classical gravity with quantum matter that avoids higher-derivative kinetic terms but predicts causality violations at high energies.

Findings

Renormalization achieved with finite couplings and field redefinitions.

Causality violations are governed by two parameters, a and b.

Tree-level causality is broken by one-loop quantum corrections.

Abstract

I prove that classical gravity coupled with quantized matter can be renormalized with a finite number of independent couplings, plus field redefinitions, without introducing higher-derivative kinetic terms in the gravitational sector, but adding vertices that couple the matter stress-tensor with the Ricci tensor. The theory is called "acausal gravity", because it predicts the violation of causality at high energies. Renormalizability is proved by means of a map M that relates acausal gravity with higher-derivative gravity. The causality violations are governed by two parameters, a and b, that are mapped by M into higher-derivative couplings. At the tree level causal prescriptions exist, but they are spoiled by the one-loop corrections. Some ideas are inspired by the usual treatments of the Abraham-Lorentz force in classical electrodynamics.