Kondo Effect in the Antiferromagnetic Quantum Critical Metal

We study the effect of a single spin-half magnetic impurity on a two dimensional metal at the antiferromagnetic quantum critical point. We use a field-theoretic functional renormalization group analysis, and perturbatively study the flow of the Kondo coupling in the regime where it is small. The recent low-energy solution of the clean quantum critical theory allows us to access the effects of critical fluctuations in a controlled manner. We find that the Kondo coupling acquires a strong momentum dependence around the Fermi surface due to the enhanced scattering near the hot spots. We comment on physical observables such as the resistivity and the shape of the Kondo cloud, as compared with the Kondo problem in Fermi liquid metals.