Abstract
The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphene-like materials, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the BPHZ prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultra-relativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity: C^*=(92-9π²)/(18π) and the anomalous dimension of the fermion field: γ_ψ(α,ξ) = 2 α(1-3ξ)/3 -16( ζ₂ N_F + 4/27 ) α² + O(α³), where α = e²/(4π)² and ξ is the gauge-fixing parameter.