A QCD analogy for quantum gravity

TL;DR

This paper explores quadratic gravity as a renormalizable, asymptotically free quantum gravity theory, drawing analogies with QCD to suggest the absence of problematic ghosts and the emergence of general relativity.

Contribution

It proposes a novel analogy between quadratic gravity and QCD, conjecturing the non-physical nature of the spin-2 ghost and discussing phase transitions and mass gap emergence.

Findings

Quadratic gravity is renormalizable and asymptotically free.

The spin-2 ghost may not appear in the physical spectrum.

A quantum phase transition may be controlled by a dimensionful parameter.

Abstract

Quadratic gravity presents us with a renormalizable, asymptotically free theory of quantum gravity. When its couplings grow strong at some scale, as in QCD, then this strong scale sets the Planck mass. QCD has a gluon that does not appear in the physical spectrum. Quadratic gravity has a spin-2 ghost that we conjecture does not appear in the physical spectrum. We discuss how the QCD analogy leads to this conjecture and to the possible emergence of general relativity. Certain aspects of the QCD path integral and its measure are also similar for quadratic gravity. With the addition of the Einstein-Hilbert term, quadratic gravity has a dimensionful parameter that seems to control a quantum phase transition and the size of a mass gap in the strong phase.