Chiral Magnetic conductivity

TL;DR

This work develops a linear-response framework to study the Chiral Magnetic Effect under time-dependent magnetic fields in a high-temperature plasma. By deriving a Kubo formula and computing the leading-order frequency- and momentum-dependent Chiral Magnetic Conductivity using a chiral-chemical-potential fermion propagator, it confirms the anomaly-fixed zero-frequency limit while revealing rich frequency-dependent structure due to pair production. The results show a notable shift from the zero-frequency value as frequency increases (toward a 1/3 reduction at small nonzero frequencies) and exhibit resonances tied to chemical potentials, providing insights relevant to heavy ion phenomenology and guiding future loop corrections, lattice, and holographic investigations.

Abstract

Gluon field configurations with nonzero topological charge generate chirality, inducing P- and CP-odd effects. When a magnetic field is applied to a system with nonzero chirality, an electromagnetic current is generated along the direction of the magnetic field. The induced current is equal to the Chiral Magnetic conductivity times the magnetic field. In this article we will compute the Chiral Magnetic conductivity of a high-temperature plasma for nonzero frequencies. This allows us to discuss the effects of time-dependent magnetic fields, such as produced in heavy ion collisions, on chirally asymmetric systems.

Figures (4)

• Figure 1: Real (red, solid) and imaginary (blue, dashed) part of the leading order Chiral Magnetic conductivity as a function of frequency, at $T=0$ and $\mu=0$ for $p=0.1\mu_5$. The result is normalized to the zero frequency conductivity $\sigma_0 = e^2 \mu_5 / (2 \pi^2)$.
• Figure 2: Real (red, solid) and imaginary (blue, dashed) part of the leading order normalized Chiral Magnetic conductivity as a function of frequency, at $T=0$, $\mu=1.5\mu_5$ and $p=0.1\mu_5$. The result is normalized to the zero frequency conductivity $\sigma_0 = e^2 \mu_5 / (2 \pi^2)$.
• Figure 3: Real (red, solid) and imaginary (blue, dashed) part of the leading order normalized Chiral Magnetic conductivity at high temperatures ($T > \mu_5$) for homogeneous magnetic fields ($p = 0$). At $\omega=0$ the normalized conductivity is equal to $1$.
• Figure 4: Induced current in time-dependent magnetic field, Eq. (\ref{['eq:magfield']}), as a function of time, at very high temperature. The results are plotted for different values of the characteristic time scale $\tau$ of the magnetic field.