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arXiv · 2009.01313

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

Nikhil Karthik·Rajamani Narayanan
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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$_3$.

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Nikhil Karthik, Rajamani Narayanan. 2020-09-02. QED$_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning. https://doi.org/10.1103/physrevlett.125.261601

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