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

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.