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 $σ_{χe}$, 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 $e\vec E$: $\vec J_A = σ_{χe} (e\vec E)$. Starting with rather general argument in the kinetic theory framework, we show how a characteristic structure $σ_{χe}\propto μμ_5$ emerges, which also indicates the CESE as an anomalous transport effect occurring only in a parity-odd environment with nonzero axial charge density $μ_5\neq 0$. Using the Hard-Thermal-Loop framework the CESE conductivity for the QGP is found to be $σ_{χe} = (\#) T\frac{{\rm Tr}_{\rm f}Q_eQ_A}{g^4\ln(1/g)} \frac{μμ_5}{T^2}$ to the leading-log accuracy with the numerical constant (#) depending on favor content, e.g. (#)$=14.5163$ for $u,d$ light flavors.

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