Holographic Chiral Magnetic Conductivity

TL;DR

This work addresses CME in hot QCD-like plasmas where perturbative methods fail. It computes the time-dependent chiral magnetic conductivity $\sigma(\omega)$ using two holographic models: (i) a fully back-reacted 5D Einstein–Maxwell theory with $U(1)_L\times U(1)_R$ and a 5D CS term encoding the axial anomaly, and (ii) the Sakai–Sugimoto model in the deconfined, chiral-symmetry-restored phase with probe branes. A finite axial chemical potential $\mu_a$ is introduced and a small external magnetic field probes the system, yielding both the static result $\sigma_0=\frac{e^2\mu_a}{2\pi^2}(N_F^{\mathrm{eff}}N_c)$ and a numerically determined finite-frequency response; the two approaches provide a robust strong-coupling complement to weak-coupling CME calculations. The findings indicate a persistent CME response at low frequencies and emphasize how CS-term definitions can affect current normalizations, informing hydrodynamic simulations of CME in RHIC-like plasmas. Together, the results establish holographic benchmarks for CME transport at strong coupling and motivate extensions to nonzero electromagnetic charge densities.

Abstract

We present holographic computations of the time-dependent chiral magnetic conductivity in the framework of gauge/gravity correspondence. Chiral magnetic effect is a phenomenon where an electromagnetic current parallel to an applied magnetic field is induced in the presence of a finite axial chemical potential. Motivated by a recent weak-coupling perturbative QCD calculation, our aim is to provide a couple of complementary computations for strongly coupled regime which might be relevant for strongly coupled RHIC plasma. We take two prototypical holographic set-ups for computing chiral magnetic conductivity; the first model is Einstein gravity with U(1)_L X U(1)_R Maxwell theory, and our second set-up is based on the Sakai-Sugimoto model in a deconfined and chiral symmetry restored phase. While the former takes into account full back-reaction while the latter not, the common feature is an important role played by the appropriate 5-dimensional Chern-Simons term corresponding to the 4-dimensional axial anomaly.

Figures (6)

• Figure 1: A schematic description of the horizon in the Eddington-Finkelstein coordinate.
• Figure 2: Frequency dependent chiral magnetic conductivity $\sigma(\omega)$ for various axial chemical potentials. The solid line is the real part of $\sigma(\omega)$ while the dashed one is the imaginary part.
• Figure 3: More results for other values of axial chemical potentials.
• Figure 4: A schematic picture of the Sakai-Sugimoto model in its deconfined and chiral symmetry restored phase.
• Figure 5: Time-dependent chiral magnetic conductivity $\sigma(\omega)$ for various axial chemical potentials in the Sakai-Sugimoto model with $T=200$ MeV. The solid line is the real part of $\sigma(\omega)$ while the dashed one is the imaginary part.