We calculate anomaly induced conductivities from a holographic gauge theory
model using Kubo formulas, making a clear conceptual distinction between
thermodynamic state variables such as chemical potentials and external
background fields. This allows us to pinpoint ambiguities in previous
holographic calculations of the chiral magnetic conductivity. We also calculate
the corresponding anomalous current three-point functions in special kinematic
regimes. We compare the holographic results to weak coupling calculations using
both dimensional regularization and cutoff regularization. In order to
reproduce the weak coupling results it is necessary to allow for singular
holographic gauge field configurations when a chiral chemical potential is
introduced for a chiral charge defined through a gauge invariant but
non-conserved chiral density. We argue that this is appropriate for actually
addressing charge separation due to the chiral magnetic effect.Comment: 17 pages, 1 figure. v2: 18 pages, 1 figure, discussion clarified
throughout the text, references added, version accepted for publication in
JHE
