Anomalous conductivity in holographic QCD

TL;DR

This work examines anomalous transport in the holographic Sakai-Sugimoto QCD model under background electromagnetic fields. By combining Karch-O'Bannon and Kubo-formula analyses, it uncovers a two-sector charge transport: one dissipative (coupled to the gluonic bath) and one non-dissipative (carried by smeared bulk 4-branes), both rooted in the axial anomaly. In the orthogonal-field setup, the longitudinal and Hall conductivities reflect this dichotomy, while in the parallel-field case the axial anomaly drives axial charge production, yielding a delta-function at zero frequency in the conductivity and signaling perfect conduction. The results illuminate how holographic QCD encodes anomaly-induced transport via horizon-based and bulk-brane charge carriers, with potential implications for real strongly coupled fermionic systems.

Abstract

We compute the longitudinal and Hall conductivities in the parallel phase of the Sakai-Sugimoto model with a transverse magnetic field. We find that the conductivities behave as if the charge of the system is made out of two different types; one behaves as charge carriers flowing through a dissipative neutral medium, while the other does not feel the dissipation. We also investigate the case of an electric field parallel to the magnetic field and find that in this case the system behaves as a perfect conductor. Both of the unusual behaviors stem from the axial anomaly.

Figures (1)

• Figure 1: The ratio of the charge $d_*$ to the total charge $d$ as a function of the magnetic field $h$ at temperature $T=0.3$.