Reduced quantum electrodynamics in curved space

The physics of graphene has provided an important connection between quantum field theory and condensed-matter physics due to the particular features of the graphene quasiparticles which can be described as massless two-dimensional Dirac fermions. An approach that has been given promising results in this context is the reduced quantum electrodynamics. In this work we consider the natural generalization of this formalism to curved spaces. As an application, we calculate the one-loop optical conductivity of graphene taking into account the presence of ripples. Such ripples are modeled by curvature effects which can be incorporated by taking into account a suitable chemical potential. In addition, we demonstrate how such effects may contribute to a decisive increase in the minimal conductivity.