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 Einstein-Hilbert 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.
Highlights
Microscopic picture has to give rise to a description of spacetime in terms of metric degrees of freedom as one flows to macroscopic scales
The enhanced symmetry is provided by an interacting renormalization group (RG) fixed point, a so-called nonGaussian fixed point (NGFP)
The coupling c, which is responsible for generating the NGFP in our case is not included in the study [206], which provides a natural explanation for the diverging results
Summary
This section reviews the basics of the functional renormalization group, currently constituting the key technical tool for investigating Asymptotic Safety (section 2.1) before summarizing the structural aspects of interacting gravity matter fixed points discussed in the literature [140, 141, 143, 157, 177, 184] in section 2.2.
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