Exact quantum scale invariance of three-dimensional reduced QED theories

An effective quantum field theory description of graphene in the ultrarelativistic regime is given by reduced quantum electrodynamics (QED) also known as pseudo QED also known as 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 conformal field theories (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 beta-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 nonsupersymmetric conformal manifold. The latter corresponds to boundary layer fermions between two different dielectric half-spaces