Magnetic conductivity and Chern-Simons Term in Holographic Hydrodynamics of Charged AdS Black Hole

TL;DR

This paper analyzes how a Chern-Simons term in the bulk RN-AdS$_5$ background alters hydrodynamic transport in the dual QGP. By decoupling vector-type perturbations via master variables and a helicity-based basis, the authors derive horizon-regular solutions in the hydrodynamic limit and show that the CS term induces a magnetic conductivity tied to the $U(1)_R$ anomaly. The boundary analysis yields explicit retarded Green functions, with off-diagonal components generating a chiral magnetic response and a DC magnetic conductivity $\sigma_B^0$ that depends on temperature and chemical potential, evolving from a finite value at low $T$ to twice that value at high $T$. These results illuminate anomaly-driven transport in holographic QGP and connect to the STU/D7-brane realizations of five-dimensional CS couplings, providing a concrete framework for studying magnetic effects in strongly coupled plasmas.

Abstract

We study the effects of the Chern-Simons term in the hydrodynamics of the five-dimensional Reissner-Nordstrom-AdS background. We work out the decoupling problem of the equations of motion and calculate the retarded Green functions explicitly. We then find that the Chern-Simons term induces the magnetic conductivity caused by the anomaly effect. It is increasing function of temperature running from a non-zero value at zero temperature to the twice the value at infinite temperature.

Figures (1)

• Figure 1: conductivities as functions of $T/{\tilde{\mu}}$. Left figure is $(\widetilde{\sigma}_B)_0$ and right one is $(\widetilde{\sigma}_E)_0$.