Phase diagram of compact QED coupled to a four-Fermi interaction

Abstract

Compact lattice quantum electrodynamics with four species of fermions is simulated with massless quarks by adding a four-Fermi interaction to the action. Simulations in the chiral limit are done on ${8}^{4}$ lattices for exploratory purposes, and ${16}^{4}$ lattices for quantitative purposes, and the phase diagram, parametrized by the gauge and the four-Fermi couplings, is mapped out. The line of monopole condensation transitions is separate from the line of chiral symmetry restoration as long as the four-Fermi coupling is not too small. The simulation results indicate that the monopole condensation transition is first order while the chiral transition is second order. The challenges in determining the universality class of the chiral transition are discussed. If the scaling region for the chiral transition is sufficiently wide, the ${16}^{4}$ simulations predict critical indices far from mean field values. We briefly discuss a speculative scenario in which antiscreening provided by strands of bound monopole and antimonopole loops is the agent that balances the screening of fermion-antifermion pairs to produce ultraviolet stable fixed points.