The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction

TL;DR

This study investigates compact lattice QED with a four-fermion interaction, showing it is logarithmically trivial and faces Landau zero charge issues, based on high-statistics finite size scaling analyses.

Contribution

It provides the first detailed finite size scaling analysis of compact QED with a four-fermion interaction, demonstrating its triviality and continuum limit behavior.

Findings

Theory is logarithmically trivial

Continuum limit suffers from Landau zero charge problem

Finite size scaling confirms triviality hypothesis

Abstract

This is the completion of an exploratory study of Compact lattice Quantum Electrodynamics with a weak four-fermi interaction and four species of massless fermions. In this formulation of Quantum Electrodynamics massless fermions can be simulated directly and Finite Size Scaling analyses can be performed at the theory's chiral symmetry breaking critical point. High statistics simulations on lattices ranging from $8^4$ to $24^4$ yield the equation of state, critical indices, scaling functions and cumulants. The measurements are well fit with the orthodox hypothesis that the theory is logarithmically trivial and its continuum limit suffers from Landau's zero charge problem.