Chiral electric separation effect in the quark-gluon plasma

In this paper we introduce and compute a new transport coefficient for the quark-gluon plasma (QGP) at very high temperature. This new coefficient ${\sigma }_{\chi e}$, the CESE (Chiral Electric Separation Effect) conductivity, quantifies the amount of axial current ${\vec{J}}_A$ that is generated in response to an externally applied electric field $e\vec{E}$: $\vec J_A = \sigma_{\chi e} (e\vec E)$. Starting with rather general argument in the kinetic theory framework, we show how a characteristic structure $\sigma_{\chi e}\propto \mu \mu_5$ emerges, which also indicates the CESE as an anomalous transport effect occurring only in a parity-odd environment with nonzero axial charge density ${\mu }_5\mathrm{\ne }0$. Using the Hard-Thermal-Loop framework the CESE conductivity for the QGP is found to be $\sigma_{\chi e} = (#) T\frac{{\rm Tr}_{\rm f}Q_eQ_A}{g^4\ln(1/g)} \frac{\mu\mu_5}{T^2}$ to the leading-log accuracy with the numerical constant (#) depending on favor content, e.g. (#)$=14.5163$ for $u,d$ light flavors.