Fractional Degrees of Freedom at Infinite Coupling in Large Nf QED in 2+1 Dimensions

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 supersymmetric Yang-Mills theory), and bear similarity to the fractional quantum Hall effect, potentially suggesting connections between these phenomena. The results found for (2 + 1)-dimensional QED are fully consistent with the expectations from particle-vortex duality.