The phases and properties of matter under global rotation have attracted much interest recently. In this Letter we investigate the pairing phenomena in a system of fermions under the presence of rotation. We find that there is a generic suppression effect on pairing states with zero angular momentum. We demonstrate this effect with the chiral condensation and the color superconductivity in hot dense QCD matter as explicit examples. In the case of chiral condensation, a new phase diagram in the temperature-rotation parameter space is found, with a nontrivial critical point.

Recently, there has been significant interest in understanding the macroscopic quantum transport in a many-body system of chiral fermions. A natural framework for describing such a system that is generally out of equilibrium is the transport equation for its phase space distribution function. In this paper, we obtain a complete solution of the covariant chiral transport for massless fermions, by starting from the general Wigner function formalism and carrying out a complete and consistent semiclassical expansion up to $\widehat{\mathbf{O}}(\hslash )$ order. In particular, we clarify certain subtle and confusing issues surrounding the Lorentz noninvariance and frame dependence associated with the three-dimensional chiral kinetic theory. We prove that such frame dependence is uniquely and completely fixed by an unambiguous definition of the $\widehat{\mathbf{O}}(\hslash )$ correction to the distribution function in each reference frame.

We show the existence of a new gapless collective excitation in a rotating fluid system with chiral fermions, named the chiral vortical wave (CVW). The CVW has its microscopic origin at the quantum anomaly and macroscopically arises from interplay between vector and axial charge fluctuations induced by vortical effects. The wave equation is obtained both from hydrodynamic current equations and from chiral kinetic theory, and its solutions show nontrivial CVW-induced charge transport from different initial conditions. Using the rotating quark-gluon plasma in heavy ion collisions as a concrete example, we show the formation of an induced flavor quadrupole in quark-gluon plasma and estimate the elliptic flow splitting effect for $\mathrm{\Lambda }$ baryons that may be experimentally measured.

In this paper we introduce and compute a new transport coefficient for the quark-gluon plasma at very high temperature. This new coefficient ${\sigma }_{\chi e}$, the chiral electric separation effect (CESE) conductivity, quantifies the amount of axial current ${\overrightarrow{J}}_A$ that is generated in response to an externally applied electric field $e\overrightarrow{E}$: ${\overrightarrow{J}}_A={\sigma }_{\chi e}(e\overrightarrow{E})$. Starting with a 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 quark-gluon plasma 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.