Asymptotically free gauged Yukawa systems

• Applicant: Professor Dr. Holger Gies
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2018 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 398579334

• Final Report Year: 2025

Final Report Abstract

Quantum field theory offers a unique property among physical theories: it can predict its own breakdown. In such a case, we expect our models to be replaced by a better description of nature above a certain maximum validity scale. Experimental elementary particle data so far is in remarkably precise agreement with the Standard Model of particle physics – a quantum field theory that appears to have such a limited validity range. Since the key structure of particle physics models is that of a gauged Yukawa system, this project has explored the possibility of such systems to feature the property of asymptotic freedom. In this case, all interactions vanish towards high energies and the corresponding model represents a ”perfect” or high-energy-complete quantum field theory which could be truly fundamental. We have identified a large class of new asymptotically free gauged Yukawa systems which share many structural properties with the standard model such as a strong-interaction sector, a chiral gauge sector, and a scalar Higgs sector. In contrast to conventional studies, we have identified high-energy complete models for which the Higgs field remains in the condensed regime along the renormalization flow towards arbitrarily short distance scales. These findings provide for a new mechanism to construct asymptotically free gauged Yukawa systems reaching conceptual consistency on all scales and being falsifiable by a comparison between experimental data and theoretical predictions for the low-energy observables. Whereas this new mechanism has not yet been able to render the running of an abelian gauge coupling (e.g. the hypercharge in the standard model) high-energy complete, we have found an alternative solution for this infamous Landau-pole problem in theories such as quantum electrodynamics: an additional Pauli spin-field coupling term can render the abelian gauge coupling asymptotically free at the expense of a quantum scale-invariant asymptotically safe Pauli coupling. While this new mechanism is remarkably robust, it’s embedding into a realistic particle-physics model remains an interesting and relevant question for future study.

Publications

• Asymptotic freedom in Z2 -YukawaQCD models. The European Physical Journal C, 79(2).
  Gies, Holger; Sondenheimer, René; Ugolotti, Alessandro & Zambelli, Luca
  
• BRST-invariant RG flows. Physical Review D, 99(8).
  Asnafi, Shimasadat; Gies, Holger & Zambelli, Luca
  
• Scheme dependence of asymptotically free solutions. The European Physical Journal C, 79(6).
  Gies, Holger; Sondenheimer, René; Ugolotti, Alessandro & Zambelli, Luca
  
• Asymptotically safe QED. The European Physical Journal C, 80(7).
  Gies, Holger & Ziebell, Jobst
  
• Critical Reflections on Asymptotically Safe Gravity. Frontiers in Physics, 8.
  Bonanno, Alfio; Eichhorn, Astrid; Gies, Holger; Pawlowski, Jan M.; Percacci, Roberto; Reuter, Martin; Saueressig, Frank & Vacca, Gian Paolo
  
• Background effective action with nonlinear massive gauge fixing. Physical Review D, 106(11).
  Gies, Holger; Gkiatas, Dimitrios & Zambelli, Luca
  
• Exploring new states of matter with a photonic emulator. Physical Review Research, 5(4).
  Karbstein, Felix; Stützer, Simon; Gies, Holger & Szameit, Alexander
  
• Pauli-term-induced fixed points in d-dimensional QED. The European Physical Journal C, 83(10).
  Gies, Holger; Tam, Kevin K. K. & Ziebell, Jobst
  
• Fermionic fixed-point structure of asymptotically safe QED with a Pauli term. The European Physical Journal C, 84(5).
  Gies, Holger & Tam, Kevin K. K.
  
• Interplay of chiral transitions in the standard model. The European Physical Journal C, 85(1).
  Gies, Holger; Schmieden, Richard & Zambelli, Luca