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

Abstract

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 GeV 2 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.