  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.
