  An appropriately oriented D3-D7-brane system is the holographic dual of
relativistic Fermions occupying a 2+1-dimensional defect embedded in
3+1-dimensional spacetime. The Fermions interact via fields of ${\mathcal N}=4$
Yang-Mills theory in the 3+1-dimensional bulk. Recently, using internal flux to
stabilize the system in the probe $N_7<<N_3$ limit, a number of solutions which
are dual to conformal field theories with Fermion content have been found. We
use holographic techniques to study perturbations of a particular one of the
conformal field theories by relevant operators. Generally, the response of a
conformal field theory to such a perturbation grows and becomes nonperturbative
at low energy scales. We shall find that a perturbation which switches on a
background magnetic field $B$ and Fermion mass $m$ induces a renormalization
group flow that can be studied perturbatively in the limit of small $m^2/B$. We
solve the leading order explicitly. We find that, for one particular value of
internal flux, the system exhibits magnetic catalysis, the spontaneous breaking
of chiral symmetry enhanced by the presence of the magnetic field. In the
process, we derive formulae predicting the Debye screening length of the
Fermion-antiFermion plasma at finite density and the diamagnetic moment of the
ground state of the Fermion system in the presence of a magnetic field.
