Lattice quantum electrodynamics for graphene

► A honeycomb lattice gauge theory for graphene is investigated. ► Anomalous critical exponents are computed by exact RG methods. ► WI and lattice symmetries guarantee the spontaneous emergence of Lorentz invariance. ► The dominant quantum instabilities are identified from first principles. ► A non-BCS gap equation for the mass is derived, suggesting strong-coupling symmetry breaking.