Fractional Degrees of Freedom at Infinite Coupling in Large N_{f} QED in 2+1 Dimensions.

Paul Romatschke

doi:10.1103/physrevlett.123.241602

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 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.

Highlights

I consider quantum electrodynamics with many electrons in 2 þ 1 space-time dimensions at finite temperature
It has been argued that the perturbative series for QED4 is divergent [2], implying that the theory becomes ambiguous at very high values of α
It is possible to use units where α 1⁄4 1, such that the weak coupling regime λ ≪ 1 corresponds to the high temperature limit, and the strong coupling regime λ ≫ 1 corresponds to the zero temperature limit

Summary

Paul Romatschke

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). It is possible to use units where α 1⁄4 1, such that the weak coupling regime λ ≪ 1 corresponds to the high temperature limit, and the strong coupling regime λ ≫ 1 corresponds to the zero temperature limit This is a common feature of pure conformal field theories in 2 þ 1 dimensions, see, e.g., the discussion in Ref. While QED3 does not have a known gravity dual, it is interesting if some of the features found for holographic theories could be understood or recovered by performing calculations purely on the field theory side at strong coupling This provides further motivation to study QED3 with many electrons.

Published by the American Physical Society

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