Topological term, QCD anomaly, and the η⁰ chiral soliton lattice in rotating baryonic matter

We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η⁰ meson and the QCD anomaly leads to an inhomogeneous condensate of the η⁰ meson, known as the chiral soliton lattice (CSL). We find that, when baryon chemical potential is much larger than isospin chemical potential, the critical angular velocity for the realization of the η⁰ CSL is much smaller than that for the π₀ CSL found previously. We also argue that the η⁰ CSL states in flavor-symmetric QCD at low density and high density should be continuously connected, extending the quark-hadron continuity conjecture in the presence of the rotation.