Holographic Anomalous Conductivities and the Chiral Magnetic Effect

TL;DR

The paper addresses anomaly-induced conductivities in a holographic gauge theory, focusing on the chiral magnetic effect (CME) and related anomalous transport. It develops a two-gauge-field holographic model with Chern-Simons terms and a Bardeen counter-term, deriving Kubo-formula conductivities: $\sigma_{\rm CME}=\frac{N_c}{2\pi^2}\mu_5$, $\sigma_{\rm axial}=\frac{N_c}{2\pi^2}\mu$, and $\sigma_{55}=\frac{N_c}{2\pi^2}\mu_5$, and nontrivial three-point functions that encode the anomaly. By comparing to weak-coupling calculations using both dimensional regularization and cutoff regularization (with a Bardeen counter-term), the authors show regulator-consistent results and identify the need to treat the chiral chemical potential $\mu_5$ as distinct from the external source $\alpha$, which can require singular bulk gauge configurations at the horizon. A key outcome is the confirmation that the axial two-point conductivity matches the CME result, $\sigma_{55}=\sigma_{CME}$, and the introduction of a novel axial conductivity, $\sigma_{55}$, whose physical interpretation may connect to charge-separation phenomena in heavy-ion collisions. Overall, the work clarifies how holography encodes anomalies, reconciles holographic and weak-coupling views, and suggests concrete observable implications for anomalous transport in strongly magnetized systems.

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.

Figures (1)

• Figure 1: The triangle diagram.