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.

Status update: asymptotically safe gravity-matter systems

“…The generated matter interactions are symmetric under the global symmetries of the kinetic terms. This observation has been explained based on the diagrammatic structure of the flow equation in [26], and has been shown more formally for shift-symmetry in scalar-gravity models in [58]. In [1] it has additionally been shown that the full global symmetry of the kinetic term for scalars is not broken to a discrete symmetry by gravity fluctuations.…”

“…When gravity is interacting, one expects that it will mediate effective matter interactions -simply because gravity fluctuations cannot be decoupled from matter. Indeed, certain matter self-interactions and non-minimal matter-gravity couplings are unavoidable at an asymptotically safe fixed point [27,23,32,11,29,39,38,16,58,35]. These interactions are determined by the global symmetries of the kinetic terms of the matter fields.…”

“…Thus, the different matter sectors distinguish a preferred and an excluded region in the gravitational parameter space. Gravitational fixed-point values lie close to the boundary of the excluded region for purely gravitational systems (where it depends on the choice of truncation, whether the gravitational fixed point ends up beyond or below the boundary [23,16,58]), but move away from this region, when appropriate matter fields (with spin 1/2 or spin 1) are added to the system [16].…”

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 self-interactions 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.…”