Chiral symmetry in quarkyonic matter

The 1/Nc expansion classifies nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region. We investigate the realization of chiral symmetry in Quarkyonic matter by taking into account condensations of chiral particle-hole pairs. It is argued that chiral symmetry and parity are locally violated by the formation of chiral spirals, <ψ-bar exp (2iμq zγ0 γz)ψ> . An extension to multiple chiral spirals is also briefly discussed.