Metallic AdS/CFT

TL;DR

This work uses AdS/CFT with probe D7-branes in an AdS-Schwarzschild background to compute the conductivity of massive N=2 hypermultiplets at finite baryon density under an external electric field. By solving the DBI action with appropriate gauge-field ansatz and infrared boundary conditions, the authors obtain a general conductivity formula that separates contributions from explicit charge carriers and thermally produced pairs, and show consistency with known weak-field and large-mass limits. They further demonstrate a Drude-like behavior in the large-mass, small-field regime and provide a straightforward generalization to Dp/Dq systems, yielding a compact universal conductivity expression. The analysis highlights the role of worldvolume horizons and the limitations imposed by the yet-incomplete phase diagram and backreaction, while suggesting avenues for applying this macroscopic holographic transport approach to other strongly coupled systems and lower-dimensional analogs.

Abstract

We use the AdS/CFT correspondence to compute the conductivity of massive N=2 hypermultiplet fields at finite baryon number density in an N=4 SU(N_c) super-Yang-Mills theory plasma in the large N_c, large 't Hooft coupling limit. The finite baryon density provides charge carriers analogous to electrons in a metal. An external electric field then induces a finite current which we determine directly. Our result for the conductivity is good for all values of the mass, external field and density, modulo statements about the yet-incomplete phase diagram. In the appropriate limits it agrees with known results obtained from analyzing small fluctuations around equilibrium. For large mass, where we expect a good quasi-particle description, we compute the drag force on the charge carriers and find that the answer is unchanged from the zero density case. Our method easily generalizes to a wide class of systems of probe branes in various backgrounds.