Renormalizing the non-renormalizable: UV fixed points from perturbation theory

• Applicant: Dr. Yannick Kluth
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 562668270

Understanding the fundamental laws of nature is one of the main challenges of modern physics. The discoveries of quantum field theory and general relativity led to some of the most precisely tested theories in the history of science. Despite this success, our current understanding of these frameworks is incomplete. The most prominent challenge is the lack of a consistent theory of quantum gravity at trans-Planckian energies. Furthermore, also the Standard Model of particle physics leads to inconsistencies in the UV. A promising approach to lift these concerns is the asymptotic safety scenario. It stipulates the existence of a UV fixed point, which renders quantum field theories well-defined and predictive, even at high energies. This makes it a promising contender as a fundamental theory of nature. However, proofs of asymptotic safety are hard to come by. While UV fixed points have been rigorously established in specific lower-dimensional models, the existence of a UV fixed point in quantum gravity is still an open question, despite a large amount of circumstantial evidence. It is often suspected that UV fixed points are inherently strongly interacting. Yet, a plethora of evidence suggests quantum gravity to exhibit a weakly interacting fixed point. This raises a pivotal question: Can UV fixed points be investigated in perturbation theory? This is of particular relevance for quantum gravity, where perturbative approaches rigorously preserve the underlying symmetries of the theory. I have successfully demonstrated the existence of a fixed point in quantum gravity in a leading order approximation of perturbation theory. This project aims at a systematic extension of this work within quantum gravity and beyond. The first step involves a proof-of-principle study using fermionic models in three dimensions. These are rigorously known to exhibit UV fixed points, providing a well-controlled testing ground to demonstrate the effectiveness of this approach. The main part focusses on quantum gravity. I will go beyond a leading order approximation in perturbation theory, which is crucial to test the robustness of a fixed point in gravity. By incorporating these subleasing contributions asymptotic safety can be established on a solid foundation. Subsequently, the impact of matter will be explored, including effects of scalar fields and electromagnetic interactions. On the one hand, this will assess which matter configurations stabilize or destabilize a perturbative fixed point of gravity. On the other hand, it will be assessed whether a UV completion of the Standard Model can be achieved through gravitational interactions.

• DFG Programme: WBP Fellowship
• International Connection: Canada
• Host: Professor Dr. Bob Holdom