Mathematics

The infrared fixed point of graphene under the renormalization groupflow is a relatively under studied yet important example of a boundaryconformal field theory with a number of remarkable properties. It hasa close relationship with three dimensional QED. It maps to itselfunder electric-magnetic duality. Moreover, it along with itssupersymmetric cousins all possess an exactly marginal coupling -- thecharge of the electron. I will review past work on this model andalso discuss my own contributions which have focused on understandingthe boundary contributions to the anomalous trace of the stress tensorand their role in helping to understand the structure of boundaryconformal field theory. I will also present some results on thehemisphere partition function for supergraphene, its dualityproperties, and an exact computation of the conductivity at arbitraryvalues of the interaction strength.