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

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${}_3$.

arXiv commentMinor changes to title and text. Version to be published in PRL

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• Bootstrapping $N_f=4$ conformal QED${}_3$
• Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid
• Conformality and self-duality of $N_f=2$ QED${}_3$
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• Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors
• Transition in the spectral gap of the massless overlap Dirac operator coupled to abelian fields in three dimensions
• Perturbative computation in a QED${}_3$-inspired conformal abelian gauge model on the lattice