Abstract
High-energy completeness of quantum electrodynamics (QED) can be induced by an interacting ultraviolet fixed point of the renormalization flow. We provide evidence for the existence of two of such fixed points in the subspace spanned by the gauge coupling, the electron mass and the Pauli spin-field coupling. Renormalization group trajectories emanating from these fixed points correspond to asymptotically safe theories that are free from the Landau pole problem. We analyze the resulting universality classes defined by the fixed points, determine the corresponding critical exponents, study the resulting phase diagram, and quantify the stability of our results with respect to a systematic expansion scheme. We also compute high-energy complete flows towards the long-range physics. We observe the existence of a renormalization group trajectory that interconnects one of the interacting fixed points with the physical low-energy behavior of QED as measured in experiment. Within pure QED, we estimate the crossover from perturbative QED to the asymptotically safe fixed point regime to occur somewhat above the Planck scale but far below the scale of the Landau pole.
Highlights
Evidence for triviality has been provided by lattice simulations [9,10,11] as well as nonperturbative functional methods [12], though the resulting picture is more involved: if quantum electrodynamics (QED) was in a strong-coupling regime at a highenergy scale, interactions would trigger chiral symmetry breaking [16,17] much in the same way as in QCD
It is fair to say that the physical relevance of such a scale remains unclear, since it is much larger than the Planck scale where the renormalization behavior of the particle physics sector is expected to be modified by quantum gravitational effects
C (2020) 80:607 be generic for models with U(1) factors; the Landau pole typically moves to smaller scales for new physics models with a larger sector of U(1)-charged scalar or fermionic particles and can drop below the Planck scale
Summary
A consistent quantum field theory only at the prize of having no interactions. evidence for triviality has been provided by lattice simulations [9,10,11] as well as nonperturbative functional methods [12], though the resulting picture is more involved (and different from the triviality arising, e.g., in φ4 theory [13,14,15]): if QED was in a strong-coupling regime at a highenergy scale , interactions would trigger chiral symmetry breaking [16,17] much in the same way as in QCD. High-energy studies typically assume asymptotic symmetry [37], as the electron mass being the source of chiral symmetry breaking (in pure QED) is implicitly assumed to be irrelevant in comparison to all other momentum scales at high energies Counterexamples to this scenario have been constructed only recently in the context of non-abelian Higgs-(Yukawa) models [38,39,40,41,42], exhibiting mass scales that grow proportionally to an (RG) scale; see [43,44] for earlier toy-model examples.
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