Electric conductivity with the magnetic field and the chiral anomaly in a holographic QCD model

TL;DR

This paper uses a holographic QCD model to study how magnetic fields and chiral anomalies affect electric conductivity in deconfined QCD matter, revealing suppression of transverse conductivity and complex behavior of longitudinal conductivity.

Contribution

It provides the first holographic analysis of electric conductivity under magnetic fields and chiral anomalies in a QCD-like model, including the regulation of divergent longitudinal conductivity.

Findings

Transverse conductivity is suppressed by up to 30% at high magnetic fields.

Longitudinal conductivity can be regulated and shows dependence on anomaly strength.

Results are consistent with lattice QCD at zero magnetic field.

Abstract

We calculate the electric conductivity $\sigma$ in deconfined QCD matter using a holographic QCD model, i.e., the Sakai-Sugimoto Model with varying magnetic field $B$ and chiral anomaly strength. After confirming that our estimated $\sigma$ for $B=0$ is consistent with the lattice-QCD results, we study the case with $B\neq 0$ in which the coefficient $\alpha$ in the Chern-Simons term controls the chiral anomaly strength. Our results imply that the transverse conductivity, $\sigma_\perp$, is suppressed to be $\lesssim 70\%$ at $B\sim 1\,\mathrm{GeV}^2$ as compared to the $B=0$ case when the temperature is fixed as $T= 0.2\,\mathrm{GeV}$. Since the Sakai-Sugimoto Model has massless fermions, the longitudinal conductivity, $\sigma_\parallel$, with $B\neq 0$ should diverge due to production of the matter chirality. Yet, it is possible to extract a regulated part out from $\sigma_\parallel$ with an extra condition to neutralize the matter chirality. This regulated quantity is interpreted as an Ohmic part of $\sigma_\parallel$. We show that the longitudinal Ohmic conductivity increases with increasing $B$ for small $\alpha$, while it is suppressed with larger $B$ for physical $\alpha=3/4$ due to anomaly induced interactions.