Dynamical color conductivity of a chiral quark-gluon plasma

TL;DR

This work computes the dynamical color conductivity of a chiral quark–gluon plasma by deriving the one-loop gluon self-energy in the hard thermal loop regime within real-time thermal field theory. The conductivity tensor is decomposed into longitudinal, transverse, and anomalous parts, with the anomalous term identified as the chiral chromomagnetic conductivity $\sigma_{\rm cmc}$, proportional to the axial imbalance $\mu_5$ and related to the topological structure of the medium. The static limit of $\sigma_{\rm cmc}$ is $\sigma_\chi = \frac{g^2}{2\pi^2}\frac{N_f}{2}\,\mu_5$, independent of $T$ and vector chemical potential $\mu$, reflecting its topological origin, while dynamical parts show characteristic frequency dependence (with space-like support for the real parts) and are only mildly affected by $\mu_5$ away from resonant regions. The results extend Abelian chiral transport to the non-Abelian QCD plasma and provide insight into how chirality-driven transport couples to chromoelectric and chromomagnetic fields, with implications for the evolution of the QGP in heavy-ion collisions.

Abstract

The dynamical chromoelectric color conductivity of a chiral plasma has been extracted from one loop gluon self energy by using linear response theory at finite temperature and density. It is shown that due to the P and CP violation the conductivity tensor has an anomalous contribution in addition to the longitudinal and transverse components. We identify this anomalous conductivity as chiral chromomagnetic conductivity. The spectral representations of real and imaginary parts of the longitudinal and transverse conductivities show marginal variations in chiral plasma as compared to the non-chiral plasma. The static limit of chiral chromomagnetic conductivity is found to be independent of medium properties reflecting its topological nature.

Figures (4)

• Figure 1: Feynman diagram for one-loop gluon self-energy
• Figure 2: (a) $\text{Re}\,\sigma_L/\overline{M_D}$ and (b) $\text{Im}\,\sigma_L/\overline{M_D}$ as a function of $\omega/q$ for two values of $\mu_5$ where $\overline{M_D}=M_D (\mu_5 = 0)$. The real part increases monotonically with frequency in the regime $\omega/q < 1$ in contrast to the imaginary part which decreases initially, increases and diverges due to the logarithmic singularity at $\omega=q$.
• Figure 3: (a) $\text{Re}\,\sigma_T/\overline{M_D}$ and (b) $\text{Im}\,\sigma_T/\overline{M_D}$ as a function of $\omega/q$ for two values of $\mu_5$ where $\overline{M_D}=M_D (\mu_5 = 0)$. The real part decreases monotonically with frequency and vanishes at $\omega/q = 1$. The imaginary part increases with frequency, reaches a maximum, and then decreases at larger values of $\omega/q$.
• Figure 4: Frequency dependence of real and imaginary part of the chiral chromo-magnetic conductivity $\sigma_{\rm cmc}$ scaled by $\sigma_\chi$, its value in the static limit, at $q=\mu_5$. Real part at $\omega \ne 0$ does not receive any contribution from the imaginary part at $\omega = 0$. As a result, for any temperature the real part of the chiral magnetic conductivity drops from $\sigma_\chi$ at $\omega = 0$ to $\sigma_\chi/3$ just away from $\omega = 0$. $\text{Im~} \sigma_{\rm cmc}$ is well behaved at large $\omega$ and is nonvanishing only for space-like kinematics ($\omega<q$).