  We study the magneto response with non-conserved currents in Holography.
Non-conserved currents are dual to massive vector fields in AdS. We introduce
the mass in a gauge invariant way via the St\"uckelberg mechanism. In
particular we find generalizations of the Chiral Magnetic Effect, the Chiral
Separation Effect and the Chiral Magnetic Wave. Since the associated charge is
not conserved we need to source it explicitly by a coupling, the generalization
of the chemical potential. In this setup we find that in general the anomalous
transport phenomena are still realized. The values we find for non-zero mass
connect however continuously to the values of the anomalous conductivities of
the consistent currents. i.e. the proper chiral magnetic effect vanishes for
all masses (as it does for the consistent current in the zero mass case)
whereas the chiral separation effect is fully present. The generalization of
the chiral magnetic wave shows that for small momenta there is no propagating
wave but two purely absorptive modes (one of them diffusive). At higher momenta
we recover the chiral magnetic wave as a combination of the two absorptive
modes. We also study the negative magneto resistivity and find that it grows
quadratically with the magnetic field. Since the (classical) $U(1)_A$ symmetry
of QCD is not at all a symmetry at the quantum level we also argue that using
massive vectors in AdS to model the axial singlet current might result in a
more realistic holographic model of QCD and should be a good starting point to
investigate the dynamics of anomalous transport in the strongly coupled quark
gluon plasma.
