Scalar-Tensor theories within Asymptotic Safety

TL;DR

This paper investigates the renormalization group flow of gravity coupled with a scalar field within the Asymptotic Safety framework, identifying a non-trivial fixed point that includes matter interactions, using non-perturbative methods.

Contribution

It provides a non-perturbative proof of the closure of shift-symmetric scalar interactions under RG flow and computes beta functions revealing a suitable fixed point for Asymptotic Safety.

Findings

Identification of an interacting fixed point with non-zero matter couplings

Demonstration of background independence in beta function calculations

First tracking of matter coupling interplay at the fixed point

Abstract

Asymptotic Safety provides an elegant mechanism for obtaining a consistent high-energy completion of gravity and gravity-matter systems. Following the initial idea by Steven Weinberg, the construction builds on an interacting fixed point of the theories renormalization group (RG) flow. In this work we use the Wetterich equation for the effective average action to investigate the RG flow of gravity supplemented by a real scalar field. We give a non-perturbative proof that the subspace of interactions respecting the global shift-symmetry of the scalar kinetic term is closed under RG transformations. Subsequently, we compute the beta functions in an approximation comprising the EinsteinHilbert action supplemented by the shift-symmetric quartic scalar self-interaction and the two lowest order shift-symmetric interactions coupling scalar-bilinears to the spacetime curvature. The computation utilizes the background field method with an arbitrary background, demonstrating that the results are manifestly background independent. Our beta functions exhibit an interacting fixed point suitable for Asymptotic Safety, where all matter interactions are non-vanishing. The presence of this fixed point is rooted in the interplay of the matter couplings which our work tracks for the first time. The relation of our findings with previous results in the literature is discussed in detail and we conclude with a brief outlook on potential phenomenological applications.