Viability of quantum-gravity induced ultraviolet completions for matter

Abstract

We highlight how the existence of an ultraviolet completion for interacting Standard-Model type matter puts constraints on the viable microscopic dynamics of asymptotically safe quantum gravity within truncated Renormalization Group flows. A first constraint -the weak-gravity bound -is rooted in the destruction of quantum scale-invariance in the matter system by strong quantumgravity fluctuations. A second constraint arises by linking Planck-scale dynamics to the dynamics at the electroweak scale. Specifically, we delineate how to extract a prediction of the top quark mass from asymptotically safe gravity and stress that a finite top mass could be difficult to accommodate in a significant part of the gravitational coupling space. I. CONNECTING QUANTUM GRAVITY TO THE ELECTROWEAK SCALEObservational guidance on the route to quantum gravity is notoriously elusive. For most "smoking-gun" signals of quantum gravity, the Planck scale would have to be accessible by controlled experiments, as effects are typically suppressed by the energy scale of the experiment over the Planck scale. Here, we discuss how to restrict the microscopic quantum-gravity dynamics by bridging the gap in the hierarchy of scales between Planck and electroweak scale in terms of a Wilsonian Renormalization Group (RG) flow. Recovering experimentally tested particle physics at the electroweak scale restricts the form of the microscopic dynamics including quantum gravity. In particular, the microscopic model could even be a fundamental quantum field theory of gravity and matter within the asymptotic-safety paradigm [1]. That scenario generalizes the success-story of asymptotic freedom -where a free RG fixed point underlies quantum scale-invariance in the ultraviolet (UV) -to an interacting UV complete theory. Based on the groundbreaking work of Reuter [2], compelling hints for asymptotic safety in pure gravity have been found , see, e.g., [42] for reviews and [43,44] for possible consequences in astrophysics and cosmology. For asymptotically safe models without gravity see, e.g., [45][46][47][48].By including matter, we derive strong hints for two structurally different constraints on the gravitational coupling space: In the UV, we find a weak-gravity bound: A quantum-gravity induced fixed point for matter can only exist for sufficiently weak quantum-gravity fluctuations. Infrared (IR) physics at the electroweak scale imposes a second constraint on the UV fixed-point structure: We demand that an observationally viable dynamics arises along an RG trajectory emanating from the fixed point. Whenever quantum fluctuations of gravity generate a negative scaling dimension for a matter coupling, e.g., a Yukawa coupling, they force it to a specific value at the Planck scale. Assuming no new physics, its * a.eichhorn@thphys.uni-heidelberg.de † a.held@thphys.uni-heidelberg.de further RG flow is given by well-known Standard Model running down to the electroweak scale. This maps a microscopic fixed-point value to an IR quantity. The fixedpoint value depends on the...

Asymptotic safety of gravity with matter

“…In other words, gravity dominates by getting weak. This is in line with the weak-gravity scenario advocated recently [82,85,86]. However, its physical foundation is different.…”

“…Note that asymptotic freedom as defined in (37) matter and gauge fields coupled to gravity can not be fully asymptotically free in the matter and gauge field sector, see [72,81,82,85,86]. In the present work, this leads to a 4 vertices from higher order invariants such as ðtrF 2 Þ 2 and trF 4 with fixed point values proportional to g 2 a =ð1 þ μÞ 3 with g a ¼ g in our approximation.…”

“…It is not sufficient to rely on the fact that the matter or gauge part can be integrated out first as gravity necessarily induces nontrivial matter and gauge self-interactions at an asymptotically safe gravity fixed point [71,72,81,85,86]. If these self-interactions do not destroy asymptotic safety, the systems achieve asymptotic safety for a general number of matter or gauge fields by guaranteeing the ultraviolet dominance of graviton fluctuations.…”

“…In expansions about flat backgrounds, it was noticed that the graviton dominates over free matter field fluctuations, either via an enhancement of the graviton propagator or the growth of the graviton coupling [79]. This pattern should play a role for asymptotic safety of the fully coupled theory and for weak gravity bounds [82,85,86]. In a similar vein, the impact of quantized gravity on gauge theories has been investigated within perturbation theory [93][94][95][96][97][98] by treating gravity as an effective field theory [99] and within the asymptotic safety scenario [67][68][69].…”

Upper bound on the Abelian gauge coupling from asymptotic safety

“…Physically, marginal irrelevance means a growth of the coupling towards the ultraviolet. Asymptotically safe quantum gravity adds a contribution to the beta function of all matter couplings that is linear in the matter coupling [1,16,[33][34][35][36][37][38][39][40][41][42][43][44][45][46]. If the sign of the gravitational contribution is negative, a fundamental change is triggered in the high-energy behavior of the corresponding coupling: the UV-repulsive free fixed point is turned into a UV attractive fixed point.…”