Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity

TL;DR

This paper explores how quantum corrections in classically scale-invariant gravity theories influence vacuum states, revealing conditions for spontaneous symmetry breaking and the generation of the Planck mass, with implications for unifying gravity and particle physics.

Contribution

It demonstrates the role of gravitational radiative corrections in vacuum structure, showing how dimensional transmutation can lead to spontaneous symmetry breaking in scale-invariant gravity models.

Findings

Dimensional transmutation can produce non-zero curvature extrema.

Spontaneous generation of the Planck mass occurs via scalar vacuum expectation values.

An asymptotically free fixed point exists but does not connect to dimensional transmutation regions.

Abstract

We discuss the nature of quantum field theories involving gravity that are classically scale-invariant. We show that gravitational radiative corrections are crucial in the determination of the nature of the vacuum state in such theories, which are renormalisable, technically natural, and can be asymptotically free in all dimensionless couplings. In the pure gravity case, we discuss the role of the Gauss-Bonnet term, and we find that Dimensional Transmutation (DT) \`a la Coleman-Weinberg leads to extrema of the effective action corresponding to nonzero values of the curvature, but such that these extrema are local maxima. In even the simplest extension of the theory to include scalar fields, we show that the same phenomenon can lead to extrema that are local minima of the effective action, with both non-zero curvature and non-zero scalar vacuum expectation values, leading to spontaneous generation of the Planck mass. Although we find an asymptotically free (AF) fixed point exists, unfortunately, no running of the couplings connect the region of DT to the basin of attraction of the AF fixed point. We also find there remains a flat direction for one of the conformal modes. We suggest that in more realistic models AF and DT could be compatible, and that the same scalar vacuum expectation values could be responsible both for DT and for spontaneous breaking of a Grand Unified gauge group.