Relativity Restored: Dirac Anisotropy in QED$_3$

TL;DR

This paper demonstrates that anisotropic QED in 2+1 dimensions becomes isotropic at low energies due to renormalization effects, restoring relativistic invariance at the critical point with a specific anomalous dimension.

Contribution

It shows that anisotropic QED$_3$ renormalizes to an isotropic form at long scales, revealing spontaneous relativistic invariance restoration.

Findings

Anisotropic QED$_3$ becomes isotropic at low energies.

Relativistic invariance is spontaneously restored at the critical point.

The anomalous dimension exponent is $rac{16}{3\pi^2 N}$.

Abstract

We show that at long lengthscales and low energies and to leading order in 1/N expansion, the anisotropic QED in 2+1 dimensions renormalizes to an isotropic limit. Consequently, the (Euclidean) relativistic invariance of the theory is spontaneously restored at the isotropic critical point, characterized by the anomalous dimension exponent of the Dirac fermion propagator $\eta$. We find $\eta=16/3\pi^2 N$.