Holographic Anomalous Conductivities and the Chiral Magnetic Effect

TL;DR

This paper uses holographic gauge theory models to compute anomaly-induced conductivities and clarifies previous ambiguities, comparing results with weak coupling calculations and discussing the role of singular gauge configurations.

Contribution

It provides a detailed holographic calculation of anomalous conductivities, distinguishing thermodynamic variables from external fields, and addresses ambiguities in prior holographic approaches.

Findings

Holographic calculations match weak coupling results when singular gauge configurations are included.

Clarifies the distinction between chemical potentials and background fields in holographic models.

Identifies and resolves ambiguities in previous holographic computations of the chiral magnetic conductivity.

Abstract

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.