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

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 $B\ne 0$ 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 $B\ne 0$ 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.

9 pages, 2 figures; references added

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