Asymptotically Safe Gravity Potentially Resolves Ultraviolet Divergences in Gauge Sector

The quest to reconcile gravity with quantum mechanics continues to drive fundamental physics, as both General Relativity and the Standard Model of particle physics exhibit limitations at extremely high energies. Maksym Riabokon from the Karlsruhe Institute of Technology, Marc Schiffer from Radboud University, and Fabian Wagner from Heidelberg University, along with their colleagues, investigate whether a promising approach called asymptotically safe gravity can overcome these hurdles. Their work assesses the reliability of this theory by examining how its predictions change with arbitrary choices made during calculations, specifically the gauge and the regulator function. The team’s results reveal that, under certain conditions, the theory exhibits remarkable robustness, yielding consistent predictions independent of these unphysical parameters, and strengthening the possibility that gravity and matter can be consistently described at all energy scales through a single, unified framework.

Functional Renormalization Group and Quantum Gravity

This collection of research papers focuses on the Functional Renormalization Group (FRG), a powerful technique used to explore quantum gravity, critical phenomena, and condensed matter physics. The work highlights the versatility of FRG as a non-perturbative tool for studying a wide range of physical systems, indicating a very active and growing field of research. Key authors consistently contributing to this field include those pioneering the development and application of FRG, such as D. F. Litim, J.

A central concept is Asymptotic Safety, which proposes that these theories might remain well-behaved at all energy scales due to the existence of a stable “fixed point” governing their behaviour. The FRG method allows researchers to trace how physical quantities change with energy, revealing whether interactions strengthen or weaken, and ultimately determining if such a stable fixed point exists. A significant portion of the research applies FRG to condensed matter systems, investigating critical phenomena, interacting electron systems, and unusual behaviours not described by standard theories. This involves combining FRG with other techniques like Dynamical Mean-Field Theory to study strongly correlated electron systems. These established theories encounter difficulties when extended to extremely high energies, manifesting as divergences in their mathematical descriptions. Asymptotic Safety proposes that these theories might remain well-behaved even at these extreme energies, through the existence of a stable “fixed point”. To explore this, the team employed a functional renormalization group approach, a sophisticated technique that examines how physical quantities change with energy scale.

This method allows researchers to trace the evolution of interactions, revealing whether they strengthen or weaken at higher energies. A key innovation lies in their focus on how gravity might influence the behaviour of matter, specifically the Abelian gauge sector of the Standard Model. They hypothesized that quantum fluctuations of spacetime, induced by gravity, could counteract problematic divergences, effectively “taming” the interactions. The researchers systematically varied computational parameters to assess the robustness of their findings, ensuring that the observed results weren’t merely artefacts of these choices. By applying the principle of minimal sensitivity, they sought parameter combinations that minimized the dependence of their results on these unphysical inputs, aiming to identify a scenario where the UV completion was a genuine physical feature, independent of the specific computational details. Both of these cornerstone theories encounter problems when extended to extremely high energies, with predictions diverging to infinity. ASQG proposes a way to avoid these divergences by introducing a new type of “fixed point” in the underlying mathematical structure, potentially offering a complete and consistent description at all energy scales. A key focus of this research is understanding whether gravity can “UV-complete” the Standard Model, specifically addressing the problem in the Abelian gauge sector, a component of the electromagnetic force.

The team’s work centers on how quantum fluctuations of gravity affect the strength of this force at different energy levels. They discovered that gravitational fluctuations can contribute an “anti-screening” effect, counteracting the usual tendency of the force to become stronger at high energies. This anti-screening, if strong enough, could prevent the force from diverging. The researchers employed the Functional Renormalization Group to model this behaviour. Their results demonstrate that the gravitational contribution can induce asymptotic freedom, a state where the force becomes weaker at very high energies, but only if this gravitational contribution is positive.

They found that the strength of this gravitational contribution acts as a critical exponent, determining whether the force will remain finite. Importantly, the team investigated how sensitive these results are to arbitrary choices made within the calculations, applying a “principle of minimal sensitivity” to identify parameter values that minimize these dependencies. The team explored how sensitive the results are to unphysical choices made within the approximation scheme used, searching for ‘points of minimal sensitivity’ where these dependencies are minimized. They found that, with a minimal amount of matter, a point exists where the system exhibits minimal sensitivity across different calculation choices, suggesting a robust UV completion, a consistent theory at very high energies. Further investigation revealed that adding different types of matter, bosons and fermions, influences the regulator dependence of the system, with fermions generally increasing it and bosons reducing it.

The large number of fermions present in the Standard Model pushes these minimal sensitivity points outside the physically meaningful range, highlighting the challenges of applying this approach to a complete model. While the results offer further support for ASQG as a potential solution to the triviality problem, the authors acknowledge that systematic uncertainties remain significant, particularly when incorporating many matter fields, and the current level of approximation is not sufficient to definitively confirm a resolution. Future work, they suggest, could involve more precise calculations and the inclusion of additional terms in the approximation to improve the reliability of the results.