We study momentum relaxation due to dilute, weak impurities in a strongly coupled CFT, a truncation of the M2 brane theory. Using the AdS/CFT correspondence, we compute the relaxation time scale as a function of the background magnetic field $B$ and charge density $\rho$. The theory admits two different types of impurities. We find that for magnetic impurities, momentum relaxation due to the impurity is suppressed by a background $B$ or $\rho$. For electric impurities, due to an underlying instability in the theory toward an ordered phase, the inverse relaxation time scale increases dramatically near $\sqrt{B^2+{\rho }^2/{\sigma }_0^2}\sim 21T^2$. We compute the Nernst response for the impure theory, and comment on similarities with recent measurements in superconductors.

• Received 14 February 2008

DOI:https://doi.org/10.1103/PhysRevD.77.106009