QED$_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning

TL;DR

This paper develops a conformal lattice gauge theory inspired by QED$_3$ that exhibits critical behavior without fine-tuning, enabling study of anomalous dimensions and dualities in a non-perturbative setting.

Contribution

It introduces a non-local gauge lattice model with gauge-only degrees of freedom, demonstrating criticality and anomalous dimensions without fine-tuning, and explores universality and self-duality in QED$_3$.

Findings

Signatures of criticality in gauge observables without fine-tuning.

Induction of anomalous dimensions in fermion bilinears.

Evidence of universality and self-duality in QED$_3$.

Abstract

We construct a conformal lattice theory with only gauge degrees of freedom based on the induced non-local 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 slow-down. By coupling exactly massless fermion sources to the lattice gauge model, we demonstrate that non-trivial anomalous dimensions are induced in fermion bilinears depending on the dimensionless electric charge of the fermion. We present a proof-of-principle lattice computation of the Wilson-coefficients of various fermion bilinear three-point functions. Finally, by mapping the charge $q$ of fermion in the model to a flavor $N$ in massless QED$_3$, we point to an universality in low-lying Dirac spectrum and an evidence of self-duality of $N=2$ QED$_3$.