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

TL;DR

This study investigates the triviality of noncompact lattice QED with a four-fermion interaction, demonstrating a logarithmically trivial second order chiral phase transition and analyzing the relevance of topological excitations.

Contribution

It provides numerical evidence that the chiral transition in lattice QED with four-fermion interaction is logarithmically trivial and clarifies the role of topological objects.

Findings

The phase transition is logarithmically trivial, similar to the Nambu-Jona Lasinio model.

The four fermi coupling is shown to be irrelevant.

The width of the scaling window varies with parameters and is narrow in fermion mass.

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.