On the Chiral Magnetic Effect in Soft-Wall AdS/QCD

TL;DR

The paper analyzes the chiral magnetic effect (CME) in soft-wall AdS/QCD, finding a non-zero vector current $J^V_3$ induced by a magnetic field in the presence of a chiral chemical potential $\mu_5$, unlike the zero result in the Sakai–Sugimoto setup. Using the soft-wall gauge sector with Yang–Mills and Chern–Simons terms, the authors derive boundary conditions and solve for the bulk fields, identifying contributions to the CME from the CS action and from the scalar/pseudoscalar sector; the latter requires careful handling of boundary conditions and leads to an additional current $\mathcal{J}_{XAA}$. They show that the vector current divergence can be canceled by a Bardeen counterterm with a coefficient $c= -\frac{k N_c}{12\pi^2}$, yielding a vector-gauge-consistent current, while including scalar couplings modifies the CME coefficient. A dual description via a two-form field $B_{\mu\nu}$ links $\mu_5$ to the curvature $H=dB$, implying non-perturbative Schwinger-like production of magnetic strings that dynamically neutralizes $\mu_5$, with the rate highly temperature-dependent. Overall, CME in soft-wall AdS/QCD is topological in nature and robust to scalar details, but its quantitative realization depends on boundary conditions and nonperturbative dynamics, offering a nuanced view beyond the Sakai–Sugimoto result.

Abstract

The essence of the chiral magnetic effect is generation of an electric current along an external magnetic field. Recently it has been studied by Rebhan et al. within the Sakai--Sugimoto model, where it was shown to be zero. As an alternative, we calculate the chiral magnetic effect in soft-wall AdS/QCD and find a non-zero result with the natural boundary conditions. The mechanism of the dynamical neutralization of the chiral chemical potential via the string production is discussed in the dual two-form representation.