Scalar-Tensor theories within Asymptotic Safety

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.

Nonvanishing gravitational contribution to matter beta functions for vanishing dimensionful regulators

“…The setting with linear split and Landau gauge α gf → 0 is commonly used when exploring the interplay between gravity and matter couplings within the framework of asymptotically safe quantum gravity [18,21,27,[45][46][47][48][49][50][51][52][53][54][55][56][57], alternative gauge choices and parameterizations are explored in [17,22,[58][59][60]. The impact of matter on the flow of gravitational couplings was investigated in [19,[61][62][63][64][65][66][67][68][69][70][71][72][73][74][75]. (ii) "Unimodular gravity": In this setting, the conformal mode is non-dynamical, and the symmetry group (before breaking by the regulator) is the group of transverse diffeomorphisms [76][77][78][79][80][81][82][83].…”

“…5 Weak-gravity bound in the vanishing regulator limit Gravity-matter interactions can induce higher-order selfinteractions in the matter sector [17,45,46,58,75]. Consequently, there is no fixed point that is fully non-interacting in the matter sector, but interacting in the gravitational sector.…”

Renormalization Group flows between Gaussian Fixed Points

“…The properties of these FPs are summarized in Table 1. Some of these FPs had already been observed in [5][6][7].…”

“…In the chart U 1 it consists of two segments: first the line going from GFP 2 in the UV to NGFP 1 in the IR, and then the trajectory with Z2 = 0, joining NGFP 1 in the UV to GFP 1 in the IR. 6 We will be interested in the infinitely many trajectories that are contained between these two extremes, see Figure 1.…”

Relational observables in Asymptotically safe gravity

“…Rather than working with pure gravity we take Γk to depend on matter fields from which we construct the physical coordinate system X μ(x) that enters the relational observables. A simple example is the inclusion of a set of four massless scalar fields minimally coupled to gravity (see [45] for gravity coupled to matter in asymptotic safety and [51] for a more recent analysis of the fixed point existence):…”