Gauged Nambu-Jona Lasinio Studies of the Triviality of Quantum Electrodynamics

Abstract

By adding a small, irrelevant four fermi interaction to the action of noncompact lattice Quantum Electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivial, with the same systematics as the Nambu-Jona Lasinio model. The irrelevance of the four fermi coupling is established numerically. The widths of the scaling windows are examined in both the coupling constant and bare fermion mass directions in parameter space. For vanishing fermion mass we find a broad scaling window in coupling. By adding a small bare fermion mass to the action we find that the width of the scaling window in the fermion mass direction is very narrow. Only when a subdominant scaling term is added to the leading term of the equation of state are adequate fits to the data possible. The failure of past studies of lattice QED to produce equation of state fits with adequate confidence levels to seriously address the question of triviality is explained. The vacuum state of the lattice model is probed for topological excitations, such as lattice Monopoles and Dirac strings, and these objects are shown to be non-critical along the chiral transition line as long as the four fermi coupling is nonzero.

39 pages revtex, 12 figures postscript, accepted for publication in Physical Review D

Cited by in corpus (19)

• Towards a renormalizable standard model without fundamental Higgs scalar
• Renormalization flow of QED
• Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions
• Asymptotically Safe QED
• Magnetic monopole plasma phase in (2+1)d compact quantum electrodynamics with fermionic matter
• Attempts at a determination of the fine-structure constant from first principles: A brief historical overview
• The Phase Diagram of Compact QED Coupled to a Four-Fermi Interaction
• The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction
• Naturalness of asymptotically safe Higgs
• Chiral symmetry breaking and monopole dynamics in non-compact QED3 coupled to a four-fermi interaction
• Magnetic Field Effect in the Fine-Structure Constant and Electron Dynamical Mass
• Non-abelian gauged NJL models on the lattice
• Four Fermion Interactions in Non-Abelian Gauge Theory
• Matching functions for heavy particles
• Landau poles in condensed matter systems
• Kinetic Theory and Stochastic Simulation of Field Quanta
• Non-compact QED(3) coupled to a four-fermi interaction
• Quantum Simulation of QED in Coulomb Gauge
• Modified Abelian and SU(2) Wilson theories on a lattice from a non-compact regularization