Renormalizable acausal theories of classical gravity coupled with interacting quantum fields

TL;DR

This paper demonstrates the renormalizability of classical gravity theories coupled with interacting quantum fields, allowing for models with higher-dimensional vertices and curvature-dependent couplings, without higher-derivative gravitational terms.

Contribution

It introduces a method to prove renormalizability of acausal gravity-matter models with curvature-dependent couplings and derives all-order beta functions related to trace anomalies.

Findings

Renormalizability of a broad class of gravity-matter theories.

Explicit formulas for beta functions of gravitational vertices.

Observation of metric running without quantization.

Abstract

We prove the renormalizability of various theories of classical gravity coupled with interacting quantum fields. The models contain vertices with dimensionality greater than four, a finite number of matter operators and a finite or reduced number of independent couplings. An interesting class of models is obtained from ordinary power-counting renormalizable theories, letting the couplings depend on the scalar curvature R of spacetime. The divergences are removed without introducing higher-derivative kinetic terms in the gravitational sector. The metric tensor has a non-trivial running, even if it is not quantized. The results are proved applying a certain map that converts classical instabilities, due to higher derivatives, into classical violations of causality, whose effects become observable at sufficiently high energies. We study acausal Einstein-Yang-Mills theory with an R-dependent gauge coupling in detail. We derive all-order formulas for the beta functions of the dimensionality-six gravitational vertices induced by renormalization. Such beta functions are related to the trace-anomaly coefficients of the matter subsector.