Holographic (pinned) stripes and magnetic effects

The D3-D7' probe-brane model provides a laboratory where the dynamics of strongly coupled fermions in 2+1 dimensions can be investigated in a controlled fashion. At large chemical potential the ground state of the model is a combined charge and spin density wave, which breaks spontaneously translation symmetry. The resulting Goldstone mode, associated with the sliding of the stripes, dominates the fluctuations driven by an infinitesimal electric field at small frequencies. Additional explicit breaking of translation invariance pins the stripes, affecting drastically the AC and DC conductivities. I study numerically this effect, and the effect of an external magnetic field, and find agreement with analytic formulas. The DC conductivities as a function of magnetic field obey a semi-circle law, which differs, however, from similar such laws typically observed in transitions between quantum Hall states.