Hosted by: Laura Classen

Dirac fermions appear as quasi-particle excitations in various condensed-matter systems for example in graphene or as surface states of topological insulators. Close to a quantum phase transition they exhibit a series of exotic properties, e.g., emergent symmetries, fluctuation-induced critical points, the appearance of two length scales and a hierarchy of mass gaps. I discuss mechanisms that are behind these phenomena from a quantum field-theoretical point of view. Further, I present a four-loop renormalization group study for the determination of the Dirac fermions' critical behavior and compare to the predictions of complementary approaches such as quantum Monte Carlo and the conformal bootstrap. Finally, I will also comment on the possibility to test duality conjectures with these calculations.