On the exact quantum scale invariance of three-dimensional reduced QED theories

TL;DR

This paper proves that reduced QED in three dimensions is an exact conformal field theory with a vanishing beta function, confirming its scale invariance and extending its conformal properties beyond perturbation theory.

Contribution

It provides a non-perturbative proof of the exact scale invariance of reduced QED, establishing it as an interacting conformal field theory and identifying a conformal manifold.

Findings

Reduced QED has a vanishing beta function, confirming exact scale invariance.

The theory can be extended to a conformal manifold via an exactly marginal deformation.

The results apply to both two- and four-component spinor formulations.

Abstract

An effective quantum field theory description of graphene in the ultra-relativistic regime is given by reduced QED aka. pseudo QED aka. mixed-dimensional QED. It has been speculated in the literature that reduced QED constitutes an example of a specific class of hard-to-find theories: an interacting CFT in more than two dimensions. This speculation was based on two-loop perturbation theory. Here, we give a proof of this feature, namely the exact vanishing of the b-function, thereby showing that reduced QED can effectively be considered as an interacting (boundary) CFT, underpinning recent work in this area. The argument, valid for both two- and four-component spinors, also naturally extends to an exactly marginal deformation of reduced QED, thence resulting in a non-supersymmetric conformal manifold. The latter corresponds to boundary layer fermions between two different dielectric half-spaces.