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