# Fractionalized Degrees of Freedom at Infinite Coupling in large Nf QED in 2+1 dimensions

## TL;DR

This paper analyzes large Nf QED in 2+1 dimensions at finite temperature, revealing fractionalized photon degrees of freedom at infinite coupling, which relate to phenomena like the fractional Quantum Hall effect and particle-vortex duality.

## Contribution

It demonstrates that at infinite coupling, photon degrees of freedom contribute half of their free-theory entropy, highlighting fractionalization in a solvable strongly coupled QED3 model.

## Key findings

- Photon entropy contribution is halved at infinite coupling.
- Fractional degrees of freedom resemble those in Quantum Hall systems.
- Results align with particle-vortex duality expectations.

## 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.