The nuclear matter, deconfined quark matter, and Quarkyonic matter in low
temperature region are classified based on the 1/Nc expansion. The chiral
symmetry in the Quarkyonic matter is investigated by taking into account
condensations of chiral particle-hole pairs. It is argued that the chiral
symmetry and parity are locally violated by the formation of chiral spirals, <
psibar exp(2 i mu z gamma^0 gamma^z) psi >. An extension to multiple chiral
spirals is also briefly discussed.Comment: Prepared for Hot Quark 2010, 4 page
