# Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background

## Abstract

We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a monopole-anti-monopole pair of magnetic charge ±Q separated by a distance s in a periodic L^{3} lattice, and study the low-lying eigenvalues of different lattice Dirac operators under a continuum limit defined by taking L → ∞ at fixed s/L. As the background gauge field is parity even, we look for a two-fold degeneracy of the Dirac spectrum that is expected of a continuum-like Dirac operator. The naive-Dirac operator exhibits such a parity-doubling, but breaks the degeneracy of the fermion-doubler modes for the Q lowest eigenvalues in the continuum limit. The Wilson-Dirac operator lifts the fermion-doublers but breaks the parity-doubling in the Q lowest modes even in the continuum limit. The overlap-Dirac operator shows parity-doubling of all the modes even at finite L that is devoid of fermion-doubling, and singles out as a properly regulated continuum Dirac operator in the presence of singular gauge field configurations albeit with a peculiar algorithmic issue.

- 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:
- 1573868

- Alternate Identifier(s):
- OSTI ID: 1580268

- Report Number(s):
- BNL-212435-2019-JAAM

Journal ID: ISSN 2470-0010; PRVDAQ; 094501

- Grant/Contract Number:
- SC0012704

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Karthik, Nikhil, and Narayanan, Rajamani. Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.094501.
```

```
Karthik, Nikhil, & Narayanan, Rajamani. Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background. United States. doi:10.1103/PhysRevD.100.094501.
```

```
Karthik, Nikhil, and Narayanan, Rajamani. Mon .
"Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background". United States. doi:10.1103/PhysRevD.100.094501.
```

```
@article{osti_1573868,
```

title = {Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background},

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

abstractNote = {We investigate numerically the effect of regulating fermions in the presence of singular background fields in three dimensions. For this, we couple free lattice fermions to a background compact U(1) gauge field consisting of a monopole-anti-monopole pair of magnetic charge ±Q separated by a distance s in a periodic L3 lattice, and study the low-lying eigenvalues of different lattice Dirac operators under a continuum limit defined by taking L → ∞ at fixed s/L. As the background gauge field is parity even, we look for a two-fold degeneracy of the Dirac spectrum that is expected of a continuum-like Dirac operator. The naive-Dirac operator exhibits such a parity-doubling, but breaks the degeneracy of the fermion-doubler modes for the Q lowest eigenvalues in the continuum limit. The Wilson-Dirac operator lifts the fermion-doublers but breaks the parity-doubling in the Q lowest modes even in the continuum limit. The overlap-Dirac operator shows parity-doubling of all the modes even at finite L that is devoid of fermion-doubling, and singles out as a properly regulated continuum Dirac operator in the presence of singular gauge field configurations albeit with a peculiar algorithmic issue.},

doi = {10.1103/PhysRevD.100.094501},

journal = {Physical Review D},

number = 9,

volume = 100,

place = {United States},

year = {2019},

month = {11}

}

DOI: 10.1103/PhysRevD.100.094501

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