Quarkyonic Chiral Spirals

After a brief introduction of the Quarkyonic matter, we argue a possibility of exciton and density wave condensations of chiral particle-hole pairs. Following the Gribov-Zwanziger arguments for Coulomb gauge QCD, we introduce a model of linear confinement We show that to the leading order of 1/Nc and Lambda (qcd)/ mu , our 3 +1 dimensional model with Nf flavors reduces to QCD in 1 +1 dimensions with 2Nf flavors. A doubling of flavors originates from an approximate spin SU(2) symmetry in 3 + 1 dimensional dynamics in Lambda (QCD)/ mu arrow right 0 limit. The reduced 1 + 1 dimensional model with finite density can be mapped onto that in vacuum through anomalous chiral rotation, and then can besolved. We found Quarkyonic Chiral Spiral - a chiral condensate forms locally, and varies with the spatial position, z, as < psi (combining macron) exp(2i mu z gamma 0 gamma (z)) psi >, rotating in the chiral space. This illustrates local violation but global restoration of the chiral symmetry.