Hall conductivity of flavor fields from AdS/CFT correspondence

Abstract

We use the AdS/CFT correspondence to compute a conductivity associated with massive $\mathcal{N}=2$ supersymmetric hypermultiplet fields at finite baryon density, propagating through an $\mathcal{N}=4$ supersymmetric $SU({N}_{c})$ Yang-Mills plasma in the large ${N}_{c}$, large 't Hooft coupling limit. We do so by introducing external electric and magnetic fields coupled to baryon number and computing the resulting induced current, from which we extract the conductivity tensor. At large hypermultiplet mass we compute the drag force on the charge carriers. We also compute the product of the drag coefficient with the kinetic mass, and find that the answer is unchanged from the zero-density case. The gravitational dual is a probe D7-brane, with a nontrivial world volume gauge field configuration, in an AdS-Schwarzschild background. We identify an effective horizon on the D7-brane world volume analogous to the world sheet horizon observed for strings moving in the same background. We generalize our results to a class of theories described by probe D-branes in various backgrounds.