The metric on field space, functional renormalization, and metric-torsion quantum gravity

TL;DR

This paper investigates the functional renormalization group flows in quantum gravity theories that include metric and torsion fields, highlighting the importance of a scale-dependent metric on the field space for the RG equations.

Contribution

It introduces a modified functional RG equation for metric-torsion gravity systems, emphasizing the role of a scale-dependent metric on the infinite-dimensional field manifold.

Findings

Comparison of different gravity theories on various theory spaces.

Demonstration that a scale-dependent metric is necessary for the RG equation.

Identification of the impact of torsion on the renormalization flow.

Abstract

Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein-Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and "tetrad-only" gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric-torsion system considered.