  We study the chiral phase transition in a magnetic field at finite
temperature and chemical potential within the Sakai-Sugimoto model, a
holographic top-down approach to (large-N_c) QCD. We consider the limit of a
small separation of the flavor D8-branes, which corresponds to a dual field
theory comparable to a Nambu-Jona Lasinio (NJL) model. Mapping out the surface
of the chiral phase transition in the parameter space of magnetic field
strength, quark chemical potential, and temperature, we find that for small
temperatures the addition of a magnetic field decreases the critical chemical
potential for chiral symmetry restoration - in contrast to the case of
vanishing chemical potential where, in accordance with the familiar phenomenon
of magnetic catalysis, the magnetic field favors the chirally broken phase.
This "inverse magnetic catalysis" (IMC) appears to be associated with a
previously found magnetic phase transition within the chirally symmetric phase
that shows an intriguing similarity to a transition into the lowest Landau
level. We estimate IMC to persist up to 10^{19} G at low temperatures.
