Renormalizing gravity: a new insight into an old problem

TL;DR

This paper proposes a novel approach to quantum gravity by using the spin connection instead of the metric, leading to a potentially renormalizable, ghost-free theory that allows studying gravitational analogs of particle physics phenomena.

Contribution

It introduces a new formulation of quantum gravity using the spin connection, which may resolve non-renormalizability and enables exploration of phenomena like the gravitational Higgs mechanism.

Findings

Spin connection approach can yield a ghost-free, renormalizable quantum gravity theory.

The gravitational Higgs mechanism can be studied using this new framework.

The approach suggests a possible effective reduction in spacetime dimensionality.

Abstract

It is well-known that perturbative quantum gravity is non-renormalizable. The metric or vierbein has generally been used as the variable to quantize in perturbative quantum gravity. In this essay, we show that one can use the spin connection instead, in which case it is possible to obtain a ghost-free renormalizable theory of quantum gravity. Furthermore in this approach, gravitational analogs of particle physics phenomena can be studied. In particular, we study the gravitational Higgs mechanism using spin connection as a gauge field, and show that this provides a mechanism for the effective reduction in the dimensionality of spacetime.