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

We calculate the electric conductivity σ 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 σ for B =0 is consistent with the lattice-QCD results, we study the case with B ≠0 in which the coefficient α in the Chern-Simons term controls the chiral anomaly strength. Our results imply that the transverse conductivity σ_⊥ is suppressed to be ≲70 % at B ∼1 GeV² as compared to the B =0 case when the temperature is fixed as T =0.2 GeV . Since the Sakai-Sugimoto model has massless fermions, the longitudinal conductivity σ_∥ with B ≠0 should diverge due to production of the matter chirality. Yet, it is possible to extract a regulated part out from σ_∥ with an extra condition to neutralize the matter chirality. This regulated quantity is interpreted as an Ohmic part of σ_∥. We show that the longitudinal Ohmic conductivity increases with increasing B for small α , while it is suppressed with larger B for physical α =3 /4 due to anomaly-induced interactions.