Chiral Fermions and Quantum Gravity

• Applicant: Professor Dr. Holger Gies
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2015 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 266047446

• Final Report Year: 2020

Final Report Abstract

The challenge of developing a convincing and consistent theory of quantum gravity is hampered by the lack of clear observational unambiguous data. The present project has explored the use of the well-known observation that the fundamental matter constituents are given by chiral fermions as a probe for possible quantum gravity scenarios. Chiral symmetry is an essential ingredient in elementary particle physics. It ensures that fermions with comparatively small masses can exist in Nature. On the other hand, chirality can be spontaneously broken by quantum fluctuations, as it is the case in the electroweak and strong interactions. As gravity is expected to become relevant near the Planck scale, gravity fluctuations must not break the chiral symmetry of the chiral fermions. Otherwise the observation of light fermions in our universe would not be compatible with such gravity interactions. In this project, we have interconnected the observed existence of light (chiral) fermions with generic quantum gravity scenarios. For this, we have used the established theoretical framework of quantum field theory for gravity from the viewpoint of both an effective field theory or an asymptotically safe fundamental quantum theory. With this tool, we have identified the mechanism of gravitational catalysis as a potential source of chiral symmetry breaking and fermion mass generation. From a scale-dependent analysis of this mechanism, we have derived bounds on the average spacetime curvature of local patches of spacetime which need to be respected in order to avoid possible gravitational fermion mass generation. Our bounds apply, in principle, to any quantum-gravity scenario that features a regime where an effective-field-theory description is possible. We have specifically analyzed the asymptotic-safety scenario for quantum gravity for which sufficient information for a self-consistent treatment of gravity and matter fluctuations are available. In this scenario, we find that quantum gravity in the light of our curvature bounds puts unprecedented constraints on the particle content of the matter sector. Interestingly, the particle content of the standard model of elementary particle physics turns out to be well compatible with asymptotically safe quantum gravity. By contrast, models with an enlarged sector of fermionic matter, e.g., including a 4th generation of fermions, would violate our bound and are thus disfavored from the viewpoint of asymptotically safe quantum gravity. In the course of developing the formalism to derive the curvature bounds, our computational tools have matured such that challenging computations in quantum gravity became possible that had previously been considered as too extensive. As a main result, we have been able to verify that the asymptotic-safety scenario of quantum gravity can resolve the fate of the perturbative two-loop counterterm, the so-called Goroff-Sagnotti term, which is conventionally taken as strong evidence that quantum gravity is perturbatively inconsistent. By contrast, our results demonstrate that this central issue can be resolved beyond the perturbative approximation, since gravitational fluctuations in the critical high-energy region leave this term irrelevant. This term hence remains controlled over all scales and its size can be predicted within asymptotically safe quantum gravity. We believe that this project has substantiated asymptotically safe quantum gravity as a viable proposal for a theory of quantum gravity. Moreover, the project has demonstrated that there is a compelling prospect of connecting (general) quantum-gravity scenarios to low-energy observables based on the interplay of quantum gravity with matter.

Publications

• Generalized Parametrization Dependence in Quantum Gravity, Phys. Rev. D 92, no. 8, 084020 (2015)
  H. Gies, B. Knorr and S. Lippoldt
  
• Gravitational Two-Loop Counterterm Is Asymptotically Safe, Phys. Rev. Lett. 116, no. 21, 211302 (2016)
  H. Gies, B. Knorr, S. Lippoldt and F. Saueressig
  
• Curvature bound from gravitational catalysis, Phys. Rev. D 97, no. 8, 085017 (2018)
  H. Gies and R. Martini
  
• Renormalization Group Flow of the Higgs Potential, Phil. Trans. Roy. Soc. Lond. A 376, no. 2114, 20170120 (2018)
  H. Gies and R. Sondenheimer