Color Ferromagnetism of Quark Matter and Quantum Hall States of Gluons in SU(3) Gauge Theory

We show a possibility that a color ferromagnetic state exists in SU(3) gauge theory of quark matter with two flavors. Although the state involves three types of unstable modes of gluons, all of these modes are stabilized by forming a quantum Hall state of one of the modes. We also show that at large chemical potential, a color superconducting state (2SC) appears even in the ferromagnetic state. This is because Meissner effect by condensed anti-triplet quark pairs does not work on the magnetic field in the ferromagnetic state.