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

Understand

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.