QED_{3}-Inspired Three-Dimensional Conformal Lattice Gauge Theory without Fine-Tuning.

We construct a conformal lattice theory with only gauge degrees of freedom based on the induced nonlocal gauge action in QED_{3} coupled to large number of flavors N of massless two-component Dirac fermions. This lattice system displays signatures of criticality in gauge observables, without any fine-tuning of couplings and can be studied without Monte Carlo critical slowdown. By coupling exactly massless fermion sources to the lattice gauge model, we demonstrate that nontrivial anomalous dimensions are induced in fermion bilinears depending on the dimensionless electric charge of the fermion.

Parity Anomaly Cancellation in Three-Dimensional QED with a Single Massless Dirac Fermion.

We study three-dimensional noncompact QED with a single two-component massless fermion and two infinitely massive regulator fermions of half the charge using the lattice overlap formalism. The parity anomaly is expected to cancel exactly between the massless and regulator fermions in the continuum, but this cancellation is inexact on a lattice akin to lattice chiral gauge theories. We show nonperturbatively that parity-breaking terms vanish in the continuum limit at any finite volume.