  The chiral magnetic and the chiral vortical effects are recently discovered
phenomena arising from chiral gauge and gravitational anomalies that lead to
generation of electric currents in presence of magnetic field or vorticity. The
magnitude of these effects is determined by the anomalous conductivities. These
conductivities can be calculated by the linear response theory, and in the
strong coupling limit this calculation can be carried out by the holographic
techniques. Earlier calculations in case of conformal field theories indicate
non-renormalization of these conductivities where the holographic calculation
agrees with the free field limit. We extend this holographic study to
non-conformal theories exhibiting mass-gap and confinement-deconfinement type
transitions in a holographic model based on the analytic black hole solution of
Gao and Zhang. We show that radiative corrections are also absent in these
non-conformal theories confirming indirect arguments of Jensen et al in a
direct and non-trivial fashion. There are various indications in field theory
that such radiative corrections should arise when contribution of dynamical
gluon fields to the chiral anomaly is present. Motivated by this, we seek for
such corrections in the holographic picture and argue that such corrections
indeed arise through mixing of the background and its fluctuations with the
axion and the one-form fields that couple to the flavor and probe gauge branes
through the Wess-Zumino terms. These corrections are non-vanishing when the
flavor to color ratio $N_f/N_c$ is finite, therefore they are only visible in
the Veneziano limit at large $N_c$.
