  We consider a bottom-up holographic model of QCD at finite temperature T and
magnetic field B, and study dependence of thermodynamics and CP-odd transport
on these variables. As the magnetic field couples to the flavor sector only,
one should take the Veneziano limit where the number of flavors and colors are
large while their ratio is kept fixed. We investigate the corresponding
holographic background in the approximation where the ratio of flavors to
colors is finite but small. We demonstrate that B-dependence of the entropy of
QCD is in qualitative agreement with the recent lattice studies. Finally we
study the CP-odd transport properties of this system. In particular, we
determine the Chern-Simons decay rate at finite B and T, that is an important
ingredient in the Chiral Magnetic Effect.
