Chiral electric separation effect in the quark-gluon plasma

Abstract

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 ${\mu }_5\ne 0$. Using the Hard-Thermal-Loop framework the CESE conductivity for the QGP is found to be ${\sigma }_{\chi e}=(\#)T\frac{{\mathrm{Tr}}_{\mathrm{f}}{Q}_e{Q}_A}{g^4\ln (1/g)}\frac{\mu {\mu }_5}{T^2}$ to the leading-log accuracy with the numerical constant (#) depending on favor content, e.g. (#)$=14.5163$ for $u,d$ light flavors.

Comments: V1: 14 pages,3 figures. V2: Typos corrected and two new appendices added. Matches published version