# ${\mathrm{QED}}_{3}$ -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 nonlocal gauge action in ${\mathrm{QED}}_{3}$ 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. 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 ${\mathrm{QED}}_{3}$, we point to a universality in low-lying Dirac spectrum and an evidence of self-duality of $N=2$ ${\mathrm{QED}}_{3}$.

- Authors:

- Publication Date:

- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)

- OSTI Identifier:
- 1737710

- Alternate Identifier(s):
- OSTI ID: 1762770

- Report Number(s):
- BNL-220808-2021-JAAM

Journal ID: ISSN 0031-9007; PRLTAO; 261601

- Grant/Contract Number:
- SC0012704; PHY-1913010

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 125 Journal Issue: 26; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Lower-dimensional field theories; conformal symmetry; ab initio calculations; critical exponents; lattice gauge theory

### Citation Formats

```
Karthik, Nikhil, and Narayanan, Rajamani. QED 3 -Inspired Three-Dimensional Conformal Lattice Gauge Theory without Fine-Tuning. United States: N. p., 2020.
Web. https://doi.org/10.1103/PhysRevLett.125.261601.
```

```
Karthik, Nikhil, & Narayanan, Rajamani. QED 3 -Inspired Three-Dimensional Conformal Lattice Gauge Theory without Fine-Tuning. United States. https://doi.org/10.1103/PhysRevLett.125.261601
```

```
Karthik, Nikhil, and Narayanan, Rajamani. Mon .
"QED 3 -Inspired Three-Dimensional Conformal Lattice Gauge Theory without Fine-Tuning". United States. https://doi.org/10.1103/PhysRevLett.125.261601.
```

```
@article{osti_1737710,
```

title = {QED 3 -Inspired Three-Dimensional Conformal Lattice Gauge Theory without Fine-Tuning},

author = {Karthik, Nikhil and Narayanan, Rajamani},

abstractNote = {We construct a conformal lattice theory with only gauge degrees of freedom based on the induced nonlocal gauge action in QED3 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. 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 QED3, we point to a universality in low-lying Dirac spectrum and an evidence of self-duality of N=2 QED3.},

doi = {10.1103/PhysRevLett.125.261601},

journal = {Physical Review Letters},

number = 26,

volume = 125,

place = {United States},

year = {2020},

month = {12}

}

https://doi.org/10.1103/PhysRevLett.125.261601

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