# Fractional Degrees of Freedom at Infinite Coupling in Large ${N}_{f}$ QED in $2+1$ Dimensions

## Abstract

I consider quantum electrodynamics with many electrons in 2+1 space-time dimensions at finite temperature. The relevant dimensionless interaction parameter for this theory is the fine structure constant divided by the temperature. The theory is solvable at any value of the coupling, in particular for very weak (high temperature) and infinitely strong coupling (corresponding to the zero temperature limit). Concentrating on the photon, each of its physical degrees of freedom at infinite coupling only contributes half of the free-theory value to the entropy. These fractional degrees of freedom are reminiscent of what has been observed in other strongly coupled systems (such as N=4 SYM), and bear similarity to the fractional Quantum Hall effect, potentially suggesting connections between these phenomena. The results found for QED3 are fully consistent with the expectations from particle-vortex duality.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)

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

- OSTI Identifier:
- 1579393

- Alternate Identifier(s):
- OSTI ID: 1593886

- Grant/Contract Number:
- SC0017905

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 123 Journal Issue: 24; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Finite temperature field theory; Lower-dimensional field theories; Quantum electrodynamics

### Citation Formats

```
Romatschke, Paul. Fractional Degrees of Freedom at Infinite Coupling in Large N f QED in 2 + 1 Dimensions. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.123.241602.
```

```
Romatschke, Paul. Fractional Degrees of Freedom at Infinite Coupling in Large N f QED in 2 + 1 Dimensions. United States. https://doi.org/10.1103/PhysRevLett.123.241602
```

```
Romatschke, Paul. Thu .
"Fractional Degrees of Freedom at Infinite Coupling in Large N f QED in 2 + 1 Dimensions". United States. https://doi.org/10.1103/PhysRevLett.123.241602.
```

```
@article{osti_1579393,
```

title = {Fractional Degrees of Freedom at Infinite Coupling in Large N f QED in 2 + 1 Dimensions},

author = {Romatschke, Paul},

abstractNote = {I consider quantum electrodynamics with many electrons in 2+1 space-time dimensions at finite temperature. The relevant dimensionless interaction parameter for this theory is the fine structure constant divided by the temperature. The theory is solvable at any value of the coupling, in particular for very weak (high temperature) and infinitely strong coupling (corresponding to the zero temperature limit). Concentrating on the photon, each of its physical degrees of freedom at infinite coupling only contributes half of the free-theory value to the entropy. These fractional degrees of freedom are reminiscent of what has been observed in other strongly coupled systems (such as N=4 SYM), and bear similarity to the fractional Quantum Hall effect, potentially suggesting connections between these phenomena. The results found for QED3 are fully consistent with the expectations from particle-vortex duality.},

doi = {10.1103/PhysRevLett.123.241602},

journal = {Physical Review Letters},

number = 24,

volume = 123,

place = {United States},

year = {2019},

month = {12}

}

https://doi.org/10.1103/PhysRevLett.123.241602

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